{"id":1269,"date":"2018-12-11T13:23:39","date_gmt":"2018-12-11T18:23:39","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/chapter\/solve-a-formula-for-a-specific-variable-2\/"},"modified":"2018-12-11T13:23:39","modified_gmt":"2018-12-11T18:23:39","slug":"solve-a-formula-for-a-specific-variable-2","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/chapter\/solve-a-formula-for-a-specific-variable-2\/","title":{"raw":"Solve a Formula for a Specific Variable","rendered":"Solve a Formula for a Specific Variable"},"content":{"raw":"\n[latexpage]<div class=\"textbox textbox--learning-objectives\"><h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>By the end of this section, you will be able to: <ul><li>Solve a formula for a specific variable<\/li><li>Use formulas to solve geometry applications<\/li><\/ul><\/div><div data-type=\"note\" id=\"fs-id1167830838404\" class=\"be-prepared\"><p id=\"fs-id1167826829110\">Before you get started, take this readiness quiz.<\/p><ol id=\"fs-id1167835375034\" type=\"1\"><li>Evaluate \\(2\\left(x+3\\right)\\) when \\(x=5.\\)<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/d3697553-3900-453f-8c08-8f74d55711ba#fs-id1167836530265\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><li>The length of a rectangle is three less than the width. Let <em data-effect=\"italics\">w<\/em> represent the width. Write an expression for the length of the rectangle.<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/d3697553-3900-453f-8c08-8f74d55711ba#fs-id1167836606933\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><li>Evaluate \\(\\frac{1}{2}bh\\) when \\(b=14\\) and \\(h=9.\\)<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/425620d9-51dd-45e5-8a21-953998a4a77f#fs-id1167829754333\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><\/ol><\/div><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167830979736\"><h3 data-type=\"title\">Solve a Formula for a Specific Variable<\/h3><p id=\"fs-id1167835509982\">We have all probably worked with some geometric formulas in our study of mathematics. Formulas are used in so many fields, it is important to recognize formulas and be able to manipulate them easily.<\/p><p id=\"fs-id1167830866056\">It is often helpful to solve a formula for a specific variable. If you need to put a formula in a spreadsheet, it is not unusual to have to solve it for a specific variable first. We isolate that variable on one side of the equals sign with a coefficient of one and all other variables and constants are on the other side of the equal sign.<\/p><p id=\"fs-id1167834538150\">Geometric formulas often need to be solved for another variable, too. The formula \\(V=\\frac{1}{3}\\pi {r}^{2}h\\) is used to find the <span data-type=\"term\" class=\"no-emphasis\">volume<\/span> of a right circular cone when given the radius of the base and height. In the next example, we will solve this formula for the height.<\/p><div data-type=\"example\" id=\"fs-id1167835351780\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167832015818\"><div data-type=\"problem\" id=\"fs-id1167831116495\"><p id=\"fs-id1167834515411\">Solve the formula \\(V=\\frac{1}{3}\\pi {r}^{2}h\\) for <em data-effect=\"italics\">h<\/em>.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167831872111\"><table id=\"fs-id1167828349231\" class=\"unnumbered unstyled\" summary=\"Write the formula. It is V is equal to one-third times pi times r squared times h. Clear the fractions by multiplying each side by 3. The result is 3 times V is equal to 3 times third times pi times r squared times h. Simplify. The result is 3 V is equal to pi times r squared times h. Divide both sides by pi times r squared. The result is 3 V divided by pi times r squared is equal to h.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Write the formula.<\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835595188\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_001a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Remove the fraction on the right.<\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167834423545\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_001b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Simplify.<\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835325472\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_001c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Divide both sides by \\(\\pi {r}^{2}.\\)<\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167831913473\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_001d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><\/tbody><\/table><p id=\"fs-id1167835377710\">We could now use this formula to find the height of a right circular cone when we know the volume and the radius of the base, by using the formula \\(h=\\frac{3V}{\\pi {r}^{2}}.\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167826937766\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167835237040\"><div data-type=\"problem\" id=\"fs-id1167831893290\"><p id=\"fs-id1167835310695\">Use the formula \\(A=\\frac{1}{2}bh\\) to solve for <em data-effect=\"italics\">b<\/em>.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835356655\"><p id=\"fs-id1167834340022\">\\(b=\\frac{2A}{h}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167831106692\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167835509131\"><div data-type=\"problem\" id=\"fs-id1167835354790\"><p id=\"fs-id1167835378068\">Use the formula \\(A=\\frac{1}{2}bh\\) to solve for <em data-effect=\"italics\">h<\/em>.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167831825126\"><p id=\"fs-id1167830697638\">\\(h=\\frac{2A}{b}\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1167835302021\">In the sciences, we often need to change <span data-type=\"term\" class=\"no-emphasis\">temperature<\/span> from Fahrenheit to Celsius or vice versa. If you travel in a foreign country, you may want to change the Celsius temperature to the more familiar Fahrenheit temperature.<\/p><div data-type=\"example\" id=\"fs-id1167835303530\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167835358195\"><div data-type=\"problem\" id=\"fs-id1167834063520\"><p id=\"fs-id1167831826403\">Solve the formula \\(C=\\frac{5}{9}\\left(F-32\\right)\\) for <em data-effect=\"italics\">F<\/em>.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835284989\"><table id=\"fs-id1167832054604\" class=\"unnumbered unstyled\" summary=\"Write the formula. It is C is equal to five-ninths times the quantity F minus 32. Clear the fractions by multiplying each side by nine-fifths C is equal to nine-fifths time s five-ninths times the quantity F minus 32. Simplify. The result is nine-fifths C is equal to F minus 32. Add 32 to both sides. The result is nine-fifths C plus 32 is equal to F. We can now use the formula F is equal to nine-fifths C plus 32 to find the Fahrenheit temperature when we know the Celsius.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Write the formula.<\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167834063097\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_002a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Remove the fraction on the right.<\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835192392\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_002b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Simplify.<\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167834130526\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_002c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Add 32 to both sides.<\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835421279\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_002d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><\/tbody><\/table><p id=\"fs-id1167831106790\">We can now use the formula \\(F=\\frac{9}{5}C+32\\) to find the Fahrenheit temperature when we know the Celsius temperature.<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167835377185\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167835303972\"><div data-type=\"problem\" id=\"fs-id1167831832047\"><p id=\"fs-id1167835380142\">Solve the formula \\(F=\\frac{9}{5}C+32\\) for <em data-effect=\"italics\">C<\/em>.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835311501\"><p id=\"fs-id1167835534081\">\\(C=\\frac{5}{9}\\left(F-32\\right)\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167835369511\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167835381542\"><div data-type=\"problem\" id=\"fs-id1167835304190\"><p id=\"fs-id1167834429234\">Solve the formula \\(A=\\frac{1}{2}h\\left(b+B\\right)\\) for <em data-effect=\"italics\">b<\/em>.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835358252\"><p id=\"fs-id1167835362584\">\\(b=\\frac{2A-Bh}{h}\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1167835336973\">The next example uses the formula for the <span data-type=\"term\" class=\"no-emphasis\">surface area<\/span> of a right cylinder.<\/p><div data-type=\"example\" id=\"fs-id1167835308479\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167835334948\"><div data-type=\"problem\" id=\"fs-id1167831107017\"><p id=\"fs-id1167834185892\">Solve the formula \\(S=2\\pi {r}^{2}+2\\pi rh\\) for <em data-effect=\"italics\">h<\/em>.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835326559\"><table id=\"fs-id1167835609380\" class=\"unnumbered unstyled\" summary=\"Write the formula. It is S is equal to 2 times pi times r squared plus 2 times pi times r times h. Isolate the h term by subtracting 2 times pi times r squared from each side. Simplify. The result is S minus 2 times pi times r squared is equal to 2 times pi times r times h. Solve for h by dividing both sides by 2 times pi times r. The quotient of the quantity S minus 2 times pi times r squared and 2 times pi times r is equal to the quotient of 2 times pi times r times h and 2 times pi times r. Simplify. The result is the quotient of the quantity S minus 2 times pi times r squared and 2 times pi times r is equal to h.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Write the formula.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167834539276\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_003a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Isolate the <em data-effect=\"italics\">h<\/em> term by subtracting \\(2\\pi {r}^{2}\\) from each side.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835332492\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_003b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Simplify.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167831832980\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_003c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Solve for <em data-effect=\"italics\">h<\/em> by dividing both sides by \\(2\\pi r.\\)<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835321840\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_003d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Simplify.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835338667\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_003e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167830693722\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167835367654\"><div data-type=\"problem\" id=\"fs-id1167835639920\"><p id=\"fs-id1167832054166\">Solve the formula \\(A=P+Prt\\) for <em data-effect=\"italics\">t<\/em>.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167832056441\"><p id=\"fs-id1167835307993\">\\(t=\\frac{A-P}{\\text{P}r}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167834301254\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167835214381\"><div data-type=\"problem\" id=\"fs-id1167834195235\"><p id=\"fs-id1167835356631\">Solve the formula \\(A=P+Prt\\) for <em data-effect=\"italics\">r<\/em>.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835344198\"><p id=\"fs-id1167831883053\">\\(r=\\frac{A-P}{\\text{P}t}\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1167835375360\">Sometimes we might be given an equation that is solved for <em data-effect=\"italics\">y<\/em> and need to solve it for <em data-effect=\"italics\">x<\/em>, or vice versa. In the following example, we\u2019re given an equation with both <em data-effect=\"italics\">x<\/em> and <em data-effect=\"italics\">y<\/em> on the same side and we\u2019ll solve it for <em data-effect=\"italics\">y<\/em>.<\/p><div data-type=\"example\" id=\"fs-id1167835229496\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167826869989\"><div data-type=\"problem\" id=\"fs-id1167835309130\"><p id=\"fs-id1167835390378\">Solve the formula \\(8x+7y=15\\) for <em data-effect=\"italics\">y<\/em>.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835327650\"><table id=\"fs-id1167834184073\" class=\"unnumbered unstyled\" summary=\"We will isolate y on one side of the equation, 8 x plus 7 y is equal to 15. Subtract 6 x from both sides to isolate the term with y. 8 x minus 8 x plus 7 y is equal to 15 minus 8 x. Simplify. The result is 7 y is equal to 15 minus 8 x. Divided both sides y 7 to make the coefficient of y 1. 7 y divided by 7 is equal to the quantity 15 minus 8 x divided y 7. Simplify. The result is y is equal to the quantity 15 minus 8 x all divided by 7.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">We will isolate <em data-effect=\"italics\">y<\/em> on one side of the equation.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835205571\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_004a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Subtract \\(6x\\) from both sides to isolate the term with <em data-effect=\"italics\">y<\/em>.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835376882\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_004b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Simplify.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167834195971\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_004c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Divide both sides by 7 to make the coefficient of <em data-effect=\"italics\">y<\/em> one.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835347694\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_004d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Simplify.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835240731\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_004e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167830963131\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167835267517\"><div data-type=\"problem\" id=\"fs-id1167835238140\"><p id=\"fs-id1167835225799\">Solve the formula \\(4x+7y=9\\) for <em data-effect=\"italics\">y<\/em>.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167826987940\"><p id=\"fs-id1167834489799\">\\(y=\\frac{9-4x}{7}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167835229662\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167835303350\"><div data-type=\"problem\" id=\"fs-id1167835343793\"><p id=\"fs-id1167835358951\">Solve the formula \\(5x+8y=1\\) for <em data-effect=\"italics\">y<\/em>.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835254555\"><p id=\"fs-id1167834489871\">\\(y=\\frac{1-5x}{8}\\)<\/p><\/div><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167835417752\"><h3 data-type=\"title\">Use Formulas to Solve Geometry Applications<\/h3><p>In this objective we will use some common geometry formulas. We will adapt our problem solving strategy so that we can solve geometry applications. The geometry formula will name the variables and give us the equation to solve.<\/p><p id=\"fs-id1167835190527\">In addition, since these applications will all involve shapes of some sort, most people find it helpful to draw a figure and label it with the given information. We will include this in the first step of the problem solving strategy for geometry applications.<\/p><div data-type=\"note\" id=\"fs-id1167830960720\" class=\"howto\"><div data-type=\"title\">Solve geometry applications.<\/div><ol id=\"fs-id1167834395861\" type=\"1\" class=\"stepwise\"><li><strong data-effect=\"bold\">Read<\/strong> the problem and make sure all the words and ideas are understood.<\/li><li><strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/li><li><strong data-effect=\"bold\">Name<\/strong> what we are looking for by choosing a variable to represent it. Draw the figure and label it with the given information.<\/li><li><strong data-effect=\"bold\">Translate<\/strong> into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.<\/li><li><strong data-effect=\"bold\">Solve<\/strong> the equation using good algebra techniques.<\/li><li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem and make sure it makes sense.<\/li><li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li><\/ol><\/div><p id=\"fs-id1167834191598\">When we solve geometry applications, we often have to use some of the properties of the figures. We will review those properties as needed.<\/p><p id=\"fs-id1167834537836\">The next example involves the <span data-type=\"term\" class=\"no-emphasis\">area<\/span> of a triangle. The area of a triangle is one-half the base times the height. We can write this as \\(A=\\frac{1}{2}bh,\\) where <em data-effect=\"italics\">b<\/em> = length of the base and <em data-effect=\"italics\">h<\/em> = height.<\/p><span data-type=\"media\" id=\"fs-id1167835280765\" data-alt=\"The figure is a triangle with its height shown. Its base is b and its height is h. The formula for the area of the triangle is A is equal to one-half times b times h.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_005_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a triangle with its height shown. Its base is b and its height is h. The formula for the area of the triangle is A is equal to one-half times b times h.\"><\/span><div data-type=\"example\" id=\"fs-id1167832053508\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167835498231\"><div data-type=\"problem\" id=\"fs-id1167835324990\"><p id=\"fs-id1167835310355\">The area of a triangular painting is 126 square inches. The base is 18 inches. What is the height?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834246972\"><table id=\"fs-id1167832151328\" class=\"unnumbered unstyled\" summary=\"Step 1 is to read the problem. Step 2 is to identify what you are looking for. It is the height of a triangle. Step 3 is to name the height. Choose a variable to represent it. Let h be the height. Draw the figure and label it with the given information. The area is 126 square inches. The height is h and the base is 18 inches. Step 4 is to translate. Write the appropriate formula. It is A is equal to one-half times b times h. Substitute in the given information. 126 is equal to one-half times 18 times h. Step 5 is to solve the equation. 126 is equal to 9 h. Divide both sides by 9. 14 is equal h. Step 6 is to check using A is equal to one-half b times h. Is 126 equal to one-half times 18 times 14? 126 is equal to 126. The solution checks. Step 7 is to answer the question. The height of the triangle is 14 inches.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for.<\/td><td data-valign=\"top\" data-align=\"left\">height of a triangle<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name.<\/strong><\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Choose a variable to represent it.<\/td><td data-valign=\"top\" data-align=\"left\">Let \\(h=\\) the height.<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Draw the figure and label it with the given information.<\/td><td data-valign=\"top\" data-align=\"left\">Area = 126 sq. in.<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835358741\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_006a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate.<\/strong><\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Write the appropriate formula.<\/td><td data-valign=\"top\" data-align=\"left\">\\(\\phantom{\\rule{1.8em}{0ex}}A=\\frac{1}{2}bh\\)<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Substitute in the given information.<\/td><td data-valign=\"top\" data-align=\"left\">\\(\\phantom{\\rule{1em}{0ex}}126=\\frac{1}{2}\u00b718\u00b7h\\)<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<\/td><td data-valign=\"top\" data-align=\"left\">\\(\\phantom{\\rule{1em}{0ex}}126=9h\\)<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Divide both sides by 9.<\/td><td data-valign=\"top\" data-align=\"left\">\\(\\phantom{\\rule{1.5em}{0ex}}14=h\\)<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check<\/strong>.<div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{ccc}\\hfill A&amp; =\\hfill &amp; \\frac{1}{2}bh\\hfill \\\\ \\hfill 126&amp; \\stackrel{?}{=}\\hfill &amp; \\frac{1}{2}\u00b718\u00b714\\hfill \\\\ \\hfill 126&amp; =\\hfill &amp; 126\u2713\\hfill \\end{array}\\)<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td><td data-valign=\"top\" data-align=\"left\">The height of the triangle is 14 inches.<\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167835333601\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167831872255\"><div data-type=\"problem\" id=\"fs-id1167834098416\"><p id=\"fs-id1167828434993\">The area of a triangular church window is 90 square meters. The base of the window is 15 meters. What is the window\u2019s height?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835339652\"><p id=\"fs-id1167826994288\">The window\u2019s height is 12 meters.<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167835308936\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167835210509\"><div data-type=\"problem\" id=\"fs-id1167831871573\"><p id=\"fs-id1167835359458\">A triangular tent door has area 15 square feet. The height is five feet. What is the length of the base?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835595818\"><p id=\"fs-id1167832058183\">The length of the base is 6 feet.<\/p><\/div><\/div><\/div><p id=\"fs-id1167831076560\">In the next example, we will work with a <span data-type=\"term\" class=\"no-emphasis\">right triangle<\/span>. To solve for the measure of each angle, we need to use two triangle properties. In any triangle, the sum of the measures of the angles is \\(180\\text{\u00b0}.\\) We can write this as a formula: \\(m\\angle A+m\\angle B+m\\angle C=180.\\) Also, since the triangle is a right triangle, we remember that a right triangle has one \\(90\\text{\u00b0}\\) angle.<\/p><p id=\"fs-id1167834472483\">Here, we will have to define one angle in terms of another. We will wait to draw the figure until we write expressions for all the angles we are looking for.<\/p><div data-type=\"example\" id=\"fs-id1167835349183\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167835514607\"><div data-type=\"problem\" id=\"fs-id1167832058290\"><p id=\"fs-id1167835343222\">The measure of one angle of a right triangle is 40 degrees more than the measure of the smallest angle. Find the measures of all three angles.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835181009\"><table id=\"fs-id1167828420750\" class=\"unnumbered unstyled\" summary=\"Step 1 is to read the problem. Step 2 is to identify what you are looking for. It is the measures of all three angles. Step 3 is to name the variable to represent it. Let a be equal to the first angle, a plus 40 be equal to the second angle, and 90 be equal to the third angle, or the right angle. Draw the figure and label it with the given information. The figure is the triangle A B C, with A measuring a plus 40, B measuring a, and C measuring 90. Step 4 is to translate. Write the appropriate formula. The measure of A plus the measure of B plus the measure of C is equal to 180. Substitute into the formula. The result is a plus the quantity a plus 40 plus 90 is equal to 180. Step 5 is to solve the equation. 2 a plus 130 is equal to 180. 2 a is equal to 50, which is the first angle. a plus 20 is the second angle. 25 plus 20 is 45. 90 is the third angle. Step 6 is to check the solutions. Is 25 plus 45 plus 90 is equal to 180? 180 is equal to 180. The solutions check. Step 7 is to answer the question. The three angles measure 25 degrees, 45 degrees, and 90 degrees.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for.<\/td><td data-valign=\"top\" data-align=\"left\">the measures of all three angles<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name.<\/strong> Choose a variable to represent it.<\/td><td data-valign=\"top\" data-align=\"left\">\\(\\begin{array}{ccc}\\hfill \\text{Let}\\phantom{\\rule{0.2em}{0ex}}a&amp; =\\hfill &amp; {1}^{\\text{st}}\\phantom{\\rule{0.2em}{0ex}}\\text{angle.}\\hfill \\\\ \\hfill a+40&amp; =\\hfill &amp; {2}^{\\text{nd}}\\phantom{\\rule{0.2em}{0ex}}\\text{angle}\\hfill \\\\ \\hfill 90&amp; =\\hfill &amp; {3}^{\\text{rd}}\\phantom{\\rule{0.2em}{0ex}}\\text{angle (the right angle)}\\hfill \\end{array}\\)<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Draw the figure and label it with the given information.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835355270\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_007a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate.<\/strong><\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Write the appropriate formula.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167831086842\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_007b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Substitute into the formula.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835512003\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_007c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167834309725\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_007d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check<\/strong>.<div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{ccc}\\hfill 25+65+90&amp; \\stackrel{?}{=}\\hfill &amp; 180\\hfill \\\\ \\hfill 180&amp; =\\hfill &amp; 180\u2713\\hfill \\end{array}\\)<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td><td data-valign=\"top\" data-align=\"left\">The three angles measure \\(25\\text{\u00b0},65\\text{\u00b0},\\) and \\(90\\text{\u00b0}.\\)<\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167834279890\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167835310675\"><div data-type=\"problem\" id=\"fs-id1167835342932\"><p id=\"fs-id1167834193267\">The measure of one angle of a right triangle is 50 more than the measure of the smallest angle. Find the measures of all three angles.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167826996842\"><p id=\"fs-id1167835232400\">The measures of the angles are 20\u00b0, 70\u00b0, and 90\u00b0.<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167826967450\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167835329250\"><div data-type=\"problem\" id=\"fs-id1167834505390\"><p id=\"fs-id1167835330290\">The measure of one angle of a right triangle is 30 more than the measure of the smallest angle. Find the measures of all three angles.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835320678\"><p id=\"fs-id1167835231754\">The measures of the angles are 30\u00b0, 60\u00b0, and 90\u00b0.<\/p><\/div><\/div><\/div><p id=\"fs-id1167835337264\">The next example uses another important geometry formula. The <span data-type=\"term\">Pythagorean Theorem<\/span> tells how the lengths of the three sides of a right triangle relate to each other. Writing the formula in every exercise and saying it aloud as you write it may help you memorize the Pythagorean Theorem.<\/p><div data-type=\"note\" id=\"fs-id1167834185486\"><div data-type=\"title\">The Pythagorean Theorem<\/div><p id=\"fs-id1167835238717\">In any right triangle, where <em data-effect=\"italics\">a<\/em> and <em data-effect=\"italics\">b<\/em> are the lengths of the legs, and <em data-effect=\"italics\">c<\/em> is the length of the hypotenuse, the sum of the squares of the lengths of the two legs equals the square of the length of the hypotenuse.<\/p><span data-type=\"media\" id=\"fs-id1167835328326\" data-alt=\"The figure is a right triangle with sides a and b, and a hypotenuse c. a squared plus b squared is equal to c squared. In a right triangle, the sum of the squares of the lengths of the two legs equals the square of the length of the hypotenuse.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_008_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides a and b, and a hypotenuse c. a squared plus b squared is equal to c squared. In a right triangle, the sum of the squares of the lengths of the two legs equals the square of the length of the hypotenuse.\"><\/span><\/div><p id=\"fs-id1167835267622\">We will use the Pythagorean Theorem in the next example.<\/p><div data-type=\"example\" id=\"fs-id1167832054640\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167835299766\"><div data-type=\"problem\" id=\"fs-id1167835356454\"><p id=\"fs-id1167831117359\">Use the Pythagorean Theorem to find the length of the other leg in<\/p><span data-type=\"media\" id=\"fs-id1167832074734\" data-alt=\"This figure is a right triangle with one leg that is 12 units and a hypotenuse that is 13 units.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_009_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure is a right triangle with one leg that is 12 units and a hypotenuse that is 13 units.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167835215305\"><table id=\"fs-id1167835233076\" class=\"unnumbered unstyled can-break\" summary=\"Step 1 is to read the problem. Step 2 is to identify what you are looking for. We are looking for the leg of the triangle. Step is to name a variable to represent it. Let a be equal to the leg of the triangle. Label side a. Now the figure is a right triangle with one leg that is 12 units, one leg that is a, and a hypotenuse that is 13 units. Step 4 is to translate. Write the appropriate formula, a squared plus b squared is equal to c squared. Substitute, so a squared plus 12 squared is equal to 13 squared. Step 5 is to solve the equation, a squared plus 144 is equal to 169. Isolate the variable term. The result is a squared is equal to 25. Use the definition of the square root. The result is a is equal to the square root of 25. Simplify. The result is a is equal to 25. Step 6 is to check the answer. Is 5 squared plus 12 squared is equal to 13 squared? Is 25 plus 144 equal to 169? 169 is equal to 169. The solution checks. Step 7 is to answer the question. The length of the leg is 5 units.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for.<\/td><td data-valign=\"top\" data-align=\"left\">the length of the leg of the triangle<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name.<\/strong><\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Choose a variable to represent it.<\/td><td data-valign=\"top\" data-align=\"left\">Let <em data-effect=\"italics\">a<\/em> = the leg of the triangle.<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Label side <em data-effect=\"italics\">a<\/em>.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167834448625\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_010b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate.<\/strong><\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Write the appropriate formula.<div data-type=\"newline\"><br><\/div>Substitute.<\/td><td data-valign=\"top\" data-align=\"left\">\\(\\begin{array}{ccc}\\hfill {a}^{2}+{b}^{2}&amp; =\\hfill &amp; {c}^{2}\\hfill \\\\ \\hfill {a}^{2}+{12}^{2}&amp; =\\hfill &amp; {13}^{2}\\hfill \\end{array}\\)<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<div data-type=\"newline\"><br><\/div>Isolate the variable term.<div data-type=\"newline\"><br><\/div>Use the definition of square root.<div data-type=\"newline\"><br><\/div>Simplify.<\/td><td data-valign=\"top\" data-align=\"left\">\\(\\begin{array}{ccc}\\hfill {a}^{2}+{144}^{}&amp; =\\hfill &amp; 169\\hfill \\\\ \\hfill {a}^{2}&amp; =\\hfill &amp; 25\\hfill \\\\ \\hfill a&amp; =\\hfill &amp; \\sqrt{25}\\hfill \\\\ \\hfill a&amp; =\\hfill &amp; 5\\hfill \\end{array}\\)<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check.<\/strong><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167835229462\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_010a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td><td data-valign=\"top\" data-align=\"left\">The length of the leg is 5.<\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167835306569\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167826814080\"><div data-type=\"problem\" id=\"fs-id1167835341581\"><p id=\"fs-id1167835348472\">Use the Pythagorean Theorem to find the length of the leg in the figure.<\/p><span data-type=\"media\" id=\"fs-id1167834473441\" data-alt=\"The figure is a right triangle with legs that are b units and 15 units, and a hypotenuse that is 17 units.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_011_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with legs that are b units and 15 units, and a hypotenuse that is 17 units.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167835343025\"><p id=\"fs-id1167835324947\">The length of the leg is 8.<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167831871406\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167835335026\"><div data-type=\"problem\" id=\"fs-id1167835305859\"><p id=\"fs-id1167832134180\">Use the Pythagorean Theorem to find the length of the leg in the figure.<\/p><span data-type=\"media\" id=\"fs-id1167835189258\" data-alt=\"The figure is a right triangle with legs that are b units and 9 units, and a hypotenuse that is 15 units.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_012_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with legs that are b units and 9 units, and a hypotenuse that is 15 units.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167835380332\"><p id=\"fs-id1167831923652\">The length of the leg is 12.<\/p><\/div><\/div><\/div><p id=\"fs-id1167835305798\">The next example is about the <span data-type=\"term\" class=\"no-emphasis\">perimeter<\/span> of a rectangle. Since the perimeter is just the distance around the rectangle, we find the sum of the lengths of its four sides\u2014the sum of two lengths and two widths. We can write is as \\(P=2L+2W\\) where <em data-effect=\"italics\">L<\/em> is the length and \\(W\\) is the width. To solve the example, we will need to define the length in terms of the width.<\/p><div data-type=\"example\" id=\"fs-id1167834228085\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167828447182\"><div data-type=\"problem\" id=\"fs-id1167831116214\"><p id=\"fs-id1167835363342\">The length of a rectangle is six centimeters more than twice the width. The perimeter is 96 centimeters. Find the length and width.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834396437\"><table id=\"fs-id1167826857370\" class=\"unnumbered unstyled can-break\" summary=\"Step 1 is to read the problem. Step is to identify what we are looking for. We are looking for the length and width. Step 3 is to name the variable to represent the width, Let w be equal to the width. The length is six more than twice the width. So the expression 2 w plus 6 is equal to length. The figure is a rectangle with the width labeled w, a length labeled 2 w plus 6, and the perimeter labeled P is equal to 96 centimeters. Step 4 is to translate. Write the appropriate formula, P is equal to 2 L plus 2 W. Substitute in the given information. 96 is equal to the sum of 2 times the quantity 2 w plus 6 and 2 w. Step 5 is to solve the equation, 96 is equal to 4 w plus 12 plus 2 w. 96 is equal to 6 w plus 12. 84 is equal to 6 w. 14 is equal w, which is the width. 2 w plus 6 represents the length, so 2 times 14 plus 6 is 34. The length is 34 centimeters. Step 6 is to check the answers. The figure is a rectangle with its width labeled 14 centimeters and its length labeled 34 centimeters. The perimeter is given by P is equal to 2 L plus 2 W. Is 96 equal to 2 times 34 plus 2 times 14. 96 is equal to 96, so the answers check. Step 7 is to answer the question. The length is 34 centimeters and the width is 14 centimeters.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what we are looking for.<\/td><td data-valign=\"top\" data-align=\"left\">the length and the width<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name<\/strong>. Choose a variable to represent the width.<div data-type=\"newline\"><br><\/div> The length is six more than twice the width.<\/td><td data-valign=\"top\" data-align=\"left\">Let \\(\\phantom{\\rule{0.5em}{0ex}}w=\\) width.<div data-type=\"newline\"><br><\/div>\\(2w+6=\\) length<div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167835262242\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_013b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div>\\(P=96\\) cm<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate.<\/strong><\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Write the appropriate formula.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835361664\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_013c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Substitute in the given information.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167834300693\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_013d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve the equation.<\/strong><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167834213903\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_013e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6.<\/strong> Check.<div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167835194800\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_013a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{ccc}\\hfill P&amp; =\\hfill &amp; 2L+2W\\hfill \\\\ \\hfill 96&amp; \\stackrel{?}{=}\\hfill &amp; 2\u00b734+2\u00b714\\hfill \\\\ \\hfill 96&amp; =\\hfill &amp; 96\u2713\\hfill \\end{array}\\)<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer the question.<\/strong><\/td><td data-valign=\"top\" data-align=\"left\">The length is 34 cm and the width is 14 cm.<\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167835363670\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167831887552\"><div data-type=\"problem\" id=\"fs-id1167831887554\"><p id=\"fs-id1167834062321\">The length of a rectangle is seven more than twice the width. The perimeter is 110 inches. Find the length and width.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835416847\"><p id=\"fs-id1167834536082\">The length is 16 inches and the width is 39 inches.<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167834459097\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167835343966\"><div data-type=\"problem\" id=\"fs-id1167835343968\"><p id=\"fs-id1167835479496\">The width of a rectangle is eight yards less than twice the length. The perimeter is 86 yards. Find the length and width.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835414655\"><p id=\"fs-id1167835334484\">The length is 17 yards and the width is 26 yards.<\/p><\/div><\/div><\/div><p id=\"fs-id1167835343328\">The next example is about the <span data-type=\"term\" class=\"no-emphasis\">perimeter<\/span> of a triangle. Since the perimeter is just the distance around the triangle, we find the sum of the lengths of its three sides. We can write this as \\(P=a+b+c,\\) where <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em> are the lengths of the sides.<\/p><div data-type=\"example\" id=\"fs-id1167835280638\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167835280640\"><div data-type=\"problem\" id=\"fs-id1167831895002\"><p id=\"fs-id1167831895004\">One side of a triangle is three inches more than the first side. The third side is two inches more than twice the first. The perimeter is 29 inches. Find the length of the three sides of the triangle.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834190033\"><table id=\"fs-id1167832043286\" class=\"unnumbered unstyled can-break\" summary=\"Step 1 is to read the problem. Step 2 is to identify what we are looking for. We are looking for the lengths of three sides of a triangle. Step is to name a variable to represent the length of the first side. Let x be equal to the length of the first side, x plus 3 be equal to the length of the second side, and 2 x plus 2 be equal to the length of the third side. The figure is a triangle with sides labeled x, x plus 3, and 2 x plus 2, and a perimeter shown to be 29 inches. Step 4 is to translate. Write the appropriate formula, which is P is equal to a plus b plus c. Substitute in the given information. The result is 29 is equal to x plus the quantity x plus 3 plus the quantity 2 x plus 2. Step 5 is to solve the equation, 29 is equal to 4 x plus 5. 24 is equal to 4 x. 6 is equal to x, which is the length of the first side. The expression, x plus 3, is the length of the second side. The second side is 6 plus 3, which is equal to 9. The expression, 2 x plus 2, is the length of the second side. The second side is 2 times 6 plus 2, which is equal to 14. Step 6 is to check the answers. The figure is a triangle with sides labeled, 6, 9, and 14. Is 29 equal to 6 plus 9 plus 14? 29 is equal to 29, so the answers check. Step 7 is to answer the question. The lengths of the sides of the triangle are 6 inches, 9 inches, and 14 inches.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what we are looking for.<\/td><td data-valign=\"top\" data-align=\"left\">the lengths of the three sides of a triangle<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name<\/strong>. Choose a variable to<div data-type=\"newline\"><br><\/div>represent the length of the first side.<\/td><td data-valign=\"top\" data-align=\"left\">\\(\\begin{array}{ccc}\\hfill \\text{Let}\\phantom{\\rule{0.2em}{0ex}}x&amp; =\\hfill &amp; \\text{length of}\\phantom{\\rule{0.2em}{0ex}}{1}^{\\text{st}}\\phantom{\\rule{0.2em}{0ex}}\\text{side.}\\hfill \\\\ \\hfill x+3&amp; =\\hfill &amp; \\text{length of}\\phantom{\\rule{0.2em}{0ex}}{2}^{\\text{nd}}\\phantom{\\rule{0.2em}{0ex}}\\text{side}\\hfill \\\\ \\hfill 2x+2&amp; =\\hfill &amp; \\text{length of}\\phantom{\\rule{0.2em}{0ex}}{3}^{\\text{rd}}\\phantom{\\rule{0.2em}{0ex}}\\text{side}\\hfill \\end{array}\\)<div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167831081604\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_014b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate.<\/strong><div data-type=\"newline\"><br><\/div>Write the appropriate formula.<div data-type=\"newline\"><br><\/div>Substitute in the given information.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167827987478\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_014c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167826849416\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_014d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167831883329\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_014e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check.<\/strong><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167835280400\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_014a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div>\\(\\phantom{\\rule{2em}{0ex}}29\\stackrel{?}{=}6+9+14\\)<div data-type=\"newline\"><br><\/div>\\(\\phantom{\\rule{2em}{0ex}}29=29\u2713\\)<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td><td data-valign=\"top\" data-align=\"left\">The lengths of the sides of the triangle<div data-type=\"newline\"><br><\/div>are 6, 9, and 14 inches.<\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167830915027\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167830915030\"><div data-type=\"problem\" id=\"fs-id1167826874298\"><p id=\"fs-id1167826874300\">One side of a triangle is seven inches more than the first side. The third side is four inches less than three times the first. The perimeter is 28 inches. Find the length of the three sides of the triangle.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835304912\"><p id=\"fs-id1167831103756\">The lengths of the sides of the triangle are 5, 11 and 12 inches.<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167834536419\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167834289509\"><div data-type=\"problem\" id=\"fs-id1167834289512\"><p id=\"fs-id1167834289514\">One side of a triangle is three feet less than the first side. The third side is five feet less than twice the first. The perimeter is 20 feet. Find the length of the three sides of the triangle.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167832116195\"><p id=\"fs-id1167832116197\">The lengths of the sides of the triangle are 4, 7 and 9 feet.<\/p><\/div><\/div><\/div><div data-type=\"example\" id=\"fs-id1167835395545\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167834422574\"><div data-type=\"problem\" id=\"fs-id1167834422576\"><p id=\"fs-id1167834422579\">The perimeter of a rectangular soccer field is 360 feet. The length is 40 feet more than the width. Find the length and width.<\/p><span data-type=\"media\" id=\"fs-id1167835479858\" data-alt=\"The figure is an illustration of rectangular soccer field.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_015_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is an illustration of rectangular soccer field.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167835390424\"><table id=\"fs-id1167835524248\" class=\"unnumbered unstyled can-break\" summary=\"Step 1 is to read the problem. Step 2 is to identify what we are looking for. We are looking for the length and width of the soccer field. Step 3 is to name a variable to represent it. Let w be equal to the width. The length is 40 feet more than the width, so let w plus 40 be equal to the length. Draw the figure and label it with the given information. The figure is an illustration of a rectangular soccer field, its length labeled w and its width labeled w plus 40, and its perimeter given as 360 feet. Step 4 is to translate. Write the appropriate formula and substitute. The formula is P is equal to 2 L plus 2 W. 360 is equal to the sum of 2 times the quantity w plus 40 and 2 w. Step 5 is to solve the equation. 360 is equal to 2 w plus 80 plus 2 w. 360 is equal to 4 w plus 80. 280 is equal to 4 w. 70 is equal to w, which is the width of the field. The expression, w plus 40, is the length of the field. It is 70 plus 40, which is equal to 110. Step 6 is to check the answers. The perimeter is given by the formula, P is equal to 2 L plus 2 W. Is 360 equal to 2 times 110 plus 2 times 70? 360 is equal to 360, so the answers check. Step 7 is to answer the question. The length of the soccer field is 110 feet and the width is 70 feet.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what we are looking for.<\/td><td data-valign=\"top\" data-align=\"left\">the length and width of the soccer field<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name.<\/strong> Choose a variable to represent it.<div data-type=\"newline\"><br><\/div>The length is 40 feet more than the width.<div data-type=\"newline\"><br><\/div>Draw the figure and label it with the<div data-type=\"newline\"><br><\/div>given information.<\/td><td data-valign=\"top\" data-align=\"left\">Let <em data-effect=\"italics\">w<\/em> = width.<div data-type=\"newline\"><br><\/div>\\(w+40=\\) length<div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167826870028\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_016a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate<\/strong>.<div data-type=\"newline\"><br><\/div>Write the appropriate formula and<div data-type=\"newline\"><br><\/div>substitute.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835595458\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_016b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167834423262\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_016c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835199569\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_016d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check.<\/strong><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{ccc}\\hfill P&amp; =\\hfill &amp; 2L+2W\\hfill \\\\ \\hfill 360&amp; \\stackrel{?}{=}\\hfill &amp; 2\\left(110\\right)+2\\left(70\\right)\\hfill \\\\ \\hfill 360&amp; =\\hfill &amp; 360\u2713\\hfill \\end{array}\\)<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td><td data-valign=\"top\" data-align=\"left\">The length of the soccer field is 110 feet<div data-type=\"newline\"><br><\/div>and the width is 70 feet.<\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167835358387\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167835358391\"><div data-type=\"problem\" id=\"fs-id1167835358393\"><p id=\"fs-id1167834184182\">The perimeter of a rectangular swimming pool is 200 feet. The length is 40 feet more than the width. Find the length and width.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834184188\"><p id=\"fs-id1167834184190\">The length of the swimming pool is 70 feet and the width is 30 feet.<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167834535247\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167831894727\"><div data-type=\"problem\" id=\"fs-id1167831894729\"><p id=\"fs-id1167831894732\">The length of a rectangular garden is 30 yards more than the width. The perimeter is 300 yards. Find the length and width.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167826967250\"><p id=\"fs-id1167826967252\">The length of the garden is 90 yards and the width is 60 yards.<\/p><\/div><\/div><\/div><p id=\"fs-id1166401363101\">Applications of these geometric properties can be found in many everyday situations as shown in the next example.<\/p><div data-type=\"example\" id=\"fs-id1167834523812\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167834523814\"><div data-type=\"problem\" id=\"fs-id1167834523816\"><p id=\"fs-id1167835238919\">Kelvin is building a gazebo and wants to brace each corner by placing a 10\u201d piece of wood diagonally as shown.<\/p><span data-type=\"media\" id=\"fs-id1167835238924\" data-alt=\"The figure is an illustration of a gazebo whose corner forms a right triangle with a 10 inch piece of wood that is placed diagonally to brace it.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_017_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is an illustration of a gazebo whose corner forms a right triangle with a 10 inch piece of wood that is placed diagonally to brace it.\"><\/span><p id=\"fs-id1167835511283\">How far from the corner should he fasten the wood if wants the distances from the corner to be equal? Approximate to the nearest tenth of an inch.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835511288\"><table id=\"fs-id1167834079300\" class=\"unnumbered unstyled can-break\" summary=\"Step 1 is to read the problem. Step 2 is to identify what we are looking for. We are looking for the distance from the corner that the bracket should be attached. Step 3 is to name a variable to represent it. Let x be equal to the distance from the corner. Draw the figure and label it with the given information. The figure is right triangle with both sides labeled x and a hypotenuse labeled 10. Step 4 is to translate. Write the appropriate formula and substitute. The formula is a squared plus b squared is equal to c squared. By substituting, the result is x squared plus x squared is equal to 10 squared. Step 5 is to solve the equation, 2 x squared is equal to 100. Isolate the variable. The result is x squared is equal to 50. Use the definition of square root. x is equal to the square root of 50. Simplify. Approximate to the nearest tenth. The side, x, is approximately equal to 7.1. Step 6 is to check using the formula a squared plus b squared is equal to c squared. Is 7.1 squared plus 7.1 squared approximately equal to 10 squared. Yes. Step 7 is to answer the question. Kelvin should fasten each piece of wood approximately 7.1 inches from the corner.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what we are looking for.<\/td><td data-valign=\"top\" data-align=\"left\">the distance from the corner that the<div data-type=\"newline\"><br><\/div>bracket should be attached<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name.<\/strong> Choose a variable to represent it.<div data-type=\"newline\"><br><\/div>Draw the figure and label it with the given<div data-type=\"newline\"><br><\/div>information.<\/td><td data-valign=\"top\" data-align=\"left\">Let \\(x=\\) the distance from the corner.<div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167834189737\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_018a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate.<\/strong><div data-type=\"newline\"><br><\/div>Write the appropriate formula and substitute.<\/td><td data-valign=\"top\" data-align=\"left\"><div data-type=\"newline\"><br><\/div>\\({a}^{2}+{b}^{2}={c}^{2}\\)<div data-type=\"newline\"><br><\/div>\\({x}^{2}+{x}^{2}={10}^{2}\\)<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<div data-type=\"newline\"><br><\/div>Isolate the variable.<div data-type=\"newline\"><br><\/div>Use the definition of square root.<div data-type=\"newline\"><br><\/div>Simplify. Approximate to the nearest tenth.<\/td><td data-valign=\"top\" data-align=\"left\">\\(\\begin{array}{}\\\\ \\\\ \\hfill 2{x}^{2}&amp; =\\hfill &amp; 100\\hfill \\\\ \\hfill {x}^{2}&amp; =\\hfill &amp; 50\\hfill \\\\ \\hfill x&amp; =\\hfill &amp; \\sqrt{50}\\hfill \\\\ \\hfill x&amp; \\approx \\hfill &amp; 7.1\\hfill \\end{array}\\)<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check.<\/strong><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{ccc}\\hfill {a}^{2}+{b}^{2}&amp; =\\hfill &amp; {c}^{2}\\hfill \\\\ \\hfill {\\left(7.1\\right)}^{2}+{\\left(7.1\\right)}^{2}&amp; \\approx \\hfill &amp; {10}^{2}\\phantom{\\rule{1em}{0ex}}\\text{Yes.}\\hfill \\end{array}\\)<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td><td data-valign=\"top\" data-align=\"left\">Kelvin should fasten each piece of wood<div data-type=\"newline\"><br><\/div>approximately 7.1\u201d from the corner.<\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167831921173\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167831921177\"><div data-type=\"problem\" id=\"fs-id1167827958374\"><p id=\"fs-id1167827958377\">John puts the base of a 13-foot ladder five feet from the wall of his house as shown in the figure. How far up the wall does the ladder reach?<\/p><span data-type=\"media\" id=\"fs-id1167827958381\" data-alt=\"The figure is an illustration that shows a ladder placed against the wall of a house. The ladder forms a right triangle with the side of the house. The ladder is 13 feet long and the base of the ladder is 5 feet from the wall of the house.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_019_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is an illustration that shows a ladder placed against the wall of a house. The ladder forms a right triangle with the side of the house. The ladder is 13 feet long and the base of the ladder is 5 feet from the wall of the house.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167835352143\"><p id=\"fs-id1167835352145\">The ladder reaches 12 feet.<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167827987488\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167827987491\"><div data-type=\"problem\" id=\"fs-id1167827987493\"><p id=\"fs-id1167835287571\">Randy wants to attach a 17-foot string of lights to the top of the 15 foot mast of his sailboat, as shown in the figure. How far from the base of the mast should he attach the end of the light string?<\/p><span data-type=\"media\" id=\"fs-id1167835287576\" data-alt=\"The figure is an illustration of a sailboat that has a 15 foot mast. A string of lights that are 17 feet long are placed diagonally from the top of the mast.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_020_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is an illustration of a sailboat that has a 15 foot mast. A string of lights that are 17 feet long are placed diagonally from the top of the mast.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167835318900\"><p id=\"fs-id1167834539690\">He should attach the lights 8 feet from the base of the mast.<\/p><\/div><\/div><\/div><div data-type=\"note\" class=\"media-2\"><p id=\"fs-id1167835513589\">Access this online resource for additional instruction and practice with solving for a variable in literal equations.<\/p><ul id=\"fs-id1167835513593\" data-display=\"block\"><li><a href=\"https:\/\/openstax.org\/l\/37literalequat\">Solving Literal Equations<\/a><\/li><\/ul><\/div><\/div><div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167834495268\"><h3 data-type=\"title\">Key Concepts<\/h3><ul id=\"fs-id1167835347888\" data-bullet-style=\"bullet\"><li><strong data-effect=\"bold\">How To Solve Geometry Applications<\/strong><ol id=\"fs-id1167834190160\" type=\"1\" class=\"stepwise\"><li><strong data-effect=\"bold\">Read<\/strong> the problem and make sure all the words and ideas are understood.<\/li><li><strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/li><li><strong data-effect=\"bold\">Name<\/strong> what you are looking for by choosing a variable to represent it. Draw the figure and label it with the given information.<\/li><li><strong data-effect=\"bold\">Translate<\/strong> into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.<\/li><li><strong data-effect=\"bold\">Solve<\/strong> the equation using good algebra techniques.<\/li><li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem and make sure it makes sense.<\/li><li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li><\/ol><\/li><li><strong data-effect=\"bold\">The Pythagorean Theorem<\/strong><ul id=\"fs-id1167831191490\" data-bullet-style=\"open-circle\"><li>In any right triangle, where <em data-effect=\"italics\">a<\/em> and <em data-effect=\"italics\">b<\/em> are the lengths of the legs, and <em data-effect=\"italics\">c<\/em> is the length of the hypotenuse, the sum of the squares of the lengths of the two legs equals the square of the length of the hypotenuse.<div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1167835231077\" data-alt=\"The figure is a right triangle with sides a and b, and a hypotenuse c with the formula, a squared plus b squared is equal to c squared.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_021_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides a and b, and a hypotenuse c with the formula, a squared plus b squared is equal to c squared.\"><\/span> <\/li><\/ul><\/li><\/ul><\/div><div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167835356559\"><div class=\"practice-perfect\" data-depth=\"2\" id=\"fs-id1167826895638\"><h4 data-type=\"title\">Practice Makes Perfect<\/h4><p id=\"fs-id1167826895645\"><strong data-effect=\"bold\">Solve a Formula for a Specific Variable<\/strong><\/p><p id=\"fs-id1167835342505\">In the following exercises, solve the given formula for the specified variable.<\/p><div data-type=\"exercise\" id=\"fs-id1167835342508\"><div data-type=\"problem\" id=\"fs-id1167835342510\"><p id=\"fs-id1167832144313\">Solve the formula \\(C=\\pi d\\) for <em data-effect=\"italics\">d<\/em>.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167831892225\"><p id=\"fs-id1167831892227\">\\(d=\\frac{C}{\\pi }\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832054581\"><div data-type=\"problem\" id=\"fs-id1167832054583\"><p id=\"fs-id1167832099503\">Solve the formula \\(C=\\pi d\\) for \\(\\pi .\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834479640\"><div data-type=\"problem\" id=\"fs-id1167834526234\"><p id=\"fs-id1167834526236\">Solve the formula \\(V=LWH\\) for <em data-effect=\"italics\">L<\/em>.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835304084\"><p id=\"fs-id1167835304086\">\\(L=\\frac{V}{WH}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835420838\"><div data-type=\"problem\" id=\"fs-id1167835420840\"><p id=\"fs-id1167835420842\">Solve the formula \\(V=LWH\\) for <em data-effect=\"italics\">H<\/em>.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826781501\"><div data-type=\"problem\" id=\"fs-id1167826781504\"><p id=\"fs-id1167826781506\">Solve the formula \\(A=\\frac{1}{2}bh\\) for <em data-effect=\"italics\">b<\/em>.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835420974\"><p id=\"fs-id1167835420976\">\\(b=\\frac{2A}{h}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834309031\"><div data-type=\"problem\" id=\"fs-id1167834309033\"><p id=\"fs-id1167834309035\">Solve the formula \\(A=\\frac{1}{2}bh\\) for <em data-effect=\"italics\">h<\/em>.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167831911306\"><div data-type=\"problem\" id=\"fs-id1167831911308\"><p id=\"fs-id1167834190492\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(A=\\frac{1}{2}{d}_{1}{d}_{2}\\) for \\({d}_{1}.\\)<\/div><div data-type=\"solution\" id=\"fs-id1167826978562\"><p id=\"fs-id1167826978565\">\\({d}_{1}=\\frac{2A}{{d}_{2}}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167828240458\"><div data-type=\"problem\" id=\"fs-id1167828240460\"><p id=\"fs-id1167834299558\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(A=\\frac{1}{2}{d}_{1}{d}_{2}\\) for \\({d}_{2}.\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832057420\"><div data-type=\"problem\" id=\"fs-id1167832057422\"><p id=\"fs-id1167832057424\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(A=\\frac{1}{2}h\\left({b}_{1}+{b}_{2}\\right)\\) for \\({b}_{1}.\\)<\/div><div data-type=\"solution\" id=\"fs-id1167834214014\"><p id=\"fs-id1167834214016\">\\({b}_{1}=\\frac{2A}{h}-{b}_{2}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167831872472\"><div data-type=\"problem\" id=\"fs-id1167831872475\"><p id=\"fs-id1167831872477\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(A=\\frac{1}{2}h\\left({b}_{1}+{b}_{2}\\right)\\) for \\({b}_{2}.\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835331684\"><div data-type=\"problem\" id=\"fs-id1167835331686\"><p id=\"fs-id1167826998344\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(h=54t+\\frac{1}{2}a{t}^{2}\\) for <em data-effect=\"italics\">a<\/em>.<\/div><div data-type=\"solution\" id=\"fs-id1167834193737\"><p id=\"fs-id1167835333648\">\\(a=\\frac{2h-108t}{{t}^{2}}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834319817\"><div data-type=\"problem\" id=\"fs-id1167834319819\"><p id=\"fs-id1167834319822\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(h=48t+\\frac{1}{2}a{t}^{2}\\) for <em data-effect=\"italics\">a<\/em>.<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835415629\"><div data-type=\"problem\" id=\"fs-id1167831892284\"><p id=\"fs-id1167831892286\">Solve \\(180=a+b+c\\) for <em data-effect=\"italics\">a<\/em>.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834439048\"><p id=\"fs-id1167834439050\">\\(a=180-b-c\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834592990\"><div data-type=\"problem\" id=\"fs-id1167834592992\"><p id=\"fs-id1167835417763\">Solve \\(180=a+b+c\\) for <em data-effect=\"italics\">c<\/em>.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167831824332\"><div data-type=\"problem\" id=\"fs-id1167831824335\"><p id=\"fs-id1167831824337\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(A=\\frac{1}{2}pl+B\\) for <em data-effect=\"italics\">p<\/em>.<\/div><div data-type=\"solution\" id=\"fs-id1167834505436\"><p id=\"fs-id1167834505438\">\\(p=\\frac{2A-2B}{l}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835189598\"><div data-type=\"problem\" id=\"fs-id1167835189601\"><p id=\"fs-id1167835189603\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(A=\\frac{1}{2}pl+B\\) for <em data-effect=\"italics\">l<\/em>.<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835380611\"><div data-type=\"problem\" id=\"fs-id1167831894377\"><p id=\"fs-id1167831894379\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(P=2L+2W\\) for <em data-effect=\"italics\">L<\/em>.<\/div><div data-type=\"solution\" id=\"fs-id1167831112470\"><p id=\"fs-id1167831112472\">\\(L=\\frac{P-2W}{2}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835420752\"><div data-type=\"problem\" id=\"fs-id1167835420754\"><p id=\"fs-id1167835498611\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(P=2L+2W\\) for <em data-effect=\"italics\">W<\/em>.<\/div><\/div><p id=\"fs-id1167835515258\">In the following exercises, solve for the formula for <em data-effect=\"italics\">y<\/em>.<\/p><div data-type=\"exercise\" id=\"fs-id1167831824988\"><div data-type=\"problem\" id=\"fs-id1167831824990\"><p id=\"fs-id1167831824992\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(8x+y=15\\) for <em data-effect=\"italics\">y<\/em>.<\/div><div data-type=\"solution\" id=\"fs-id1167830703747\"><p id=\"fs-id1167830703749\">\\(y=15-8x\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835319368\"><div data-type=\"problem\" id=\"fs-id1167835319370\"><p id=\"fs-id1167835319372\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(9x+y=13\\) for <em data-effect=\"italics\">y<\/em>.<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832058756\"><div data-type=\"problem\" id=\"fs-id1167832058758\"><p id=\"fs-id1167832058760\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(-4x+y=-6\\) for <em data-effect=\"italics\">y<\/em>.<\/div><div data-type=\"solution\" id=\"fs-id1167831880819\"><p id=\"fs-id1167831880821\">\\(y=-6+4x\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834300891\"><div data-type=\"problem\" id=\"fs-id1167834300893\"><p id=\"fs-id1167834300895\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(-5x+y=-1\\) for <em data-effect=\"italics\">y<\/em>.<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835518375\"><div data-type=\"problem\" id=\"fs-id1167826819375\"><p id=\"fs-id1167826819377\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(x-y=-4\\) for <em data-effect=\"italics\">y<\/em>.<\/div><div data-type=\"solution\" id=\"fs-id1167834324635\"><p id=\"fs-id1167834324637\">\\(y=4+x\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835236061\"><div data-type=\"problem\" id=\"fs-id1167835236063\"><p id=\"fs-id1167835236065\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(x-y=-3\\) for <em data-effect=\"italics\">y<\/em>.<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834192344\"><div data-type=\"problem\" id=\"fs-id1167834192346\"><p id=\"fs-id1167834192349\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(4x+3y=7\\) for <em data-effect=\"italics\">y<\/em>.<\/div><div data-type=\"solution\" id=\"fs-id1167831880016\"><p id=\"fs-id1167831880018\">\\(y=\\frac{7-4x}{3}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834506155\"><div data-type=\"problem\" id=\"fs-id1167834506157\"><p id=\"fs-id1167834506160\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(3x+2y=11\\) for <em data-effect=\"italics\">y<\/em>.<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832087113\"><div data-type=\"problem\" id=\"fs-id1167830865704\"><p id=\"fs-id1167830865706\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(2x+3y=12\\) for <em data-effect=\"italics\">y<\/em>.<\/div><div data-type=\"solution\" id=\"fs-id1167828421269\"><p id=\"fs-id1167828421272\">\\(y=\\frac{12-2x}{3}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835420241\"><div data-type=\"problem\" id=\"fs-id1167835420243\"><p id=\"fs-id1167835327442\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(5x+2y=10\\) for <em data-effect=\"italics\">y<\/em>.<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832065987\"><div data-type=\"problem\" id=\"fs-id1167832065989\"><p id=\"fs-id1167832065992\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(3x-2y=18\\) for <em data-effect=\"italics\">y<\/em>.<\/div><div data-type=\"solution\" id=\"fs-id1167834428843\"><p id=\"fs-id1167834428846\">\\(y=\\frac{18-3x}{-2}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835319959\"><div data-type=\"problem\" id=\"fs-id1167835319962\"><p id=\"fs-id1167835319964\">Solve the formula<\/p><div data-type=\"newline\"><br><\/div>\\(4x-3y=12\\) for <em data-effect=\"italics\">y<\/em>.<\/div><\/div><p id=\"fs-id1167834130084\"><strong data-effect=\"bold\">Use Formulas to Solve Geometry Applications<\/strong><\/p><p id=\"fs-id1167834130091\">In the following exercises, solve using a geometry formula.<\/p><div data-type=\"exercise\" id=\"fs-id1167831894321\"><div data-type=\"problem\" id=\"fs-id1167831894323\"><p id=\"fs-id1167831894326\">A triangular flag has area 0.75 square feet and height 1.5 foot. What is its base?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167831894330\"><p id=\"fs-id1167831894332\">1 foot<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167830757264\"><div data-type=\"problem\" id=\"fs-id1167830757267\"><p id=\"fs-id1167830757269\">A triangular window has area 24 square feet and height six feet. What is its base?<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826779531\"><div data-type=\"problem\" id=\"fs-id1167826779533\"><p id=\"fs-id1167826779536\">What is the base of a triangle with area 207 square inches and height 18 inches?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167826779540\"><p id=\"fs-id1167826779542\">23 inches<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167831888080\"><div data-type=\"problem\" id=\"fs-id1167831888082\"><p id=\"fs-id1167831888084\">What is the height of a triangle with area 893 square inches and base 38 inches?<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835483782\"><div data-type=\"problem\" id=\"fs-id1167835483784\"><p id=\"fs-id1167835483786\">The two smaller angles of a right triangle have equal measures. Find the measures of all three angles.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835370677\"><p id=\"fs-id1167835370679\">\\(45\\text{\u00b0},45\\text{\u00b0},90\\text{\u00b0}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834526616\"><div data-type=\"problem\" id=\"fs-id1167834526618\"><p id=\"fs-id1167826983749\">The measure of the smallest angle of a right triangle is \\(20\\text{\u00b0}\\) less than the measure of the next larger angle. Find the measures of all three angles.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167831921553\"><div data-type=\"problem\" id=\"fs-id1167831921555\"><p id=\"fs-id1167831921557\">The angles in a triangle are such that one angle is twice the smallest angle, while the third angle is three times as large as the smallest angle. Find the measures of all three angles.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835420912\"><p id=\"fs-id1167835420914\">\\(30\\text{\u00b0},60\\text{\u00b0},90\\text{\u00b0}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834535231\"><div data-type=\"problem\" id=\"fs-id1167832042513\"><p id=\"fs-id1167832042515\">The angles in a triangle are such that one angle is 20 more than the smallest angle, while the third angle is three times as large as the smallest angle. Find the measures of all three angles.<\/p><\/div><\/div><p id=\"fs-id1167834556835\">In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse.<\/p><div data-type=\"exercise\" id=\"fs-id1167834556838\"><div data-type=\"problem\" id=\"fs-id1167834556840\"><span data-type=\"media\" id=\"fs-id1167834556841\" data-alt=\"The figure is a right triangle with sides 9 units and 12 units.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_201_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides 9 units and 12 units.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167835359874\"><p id=\"fs-id1167835359876\">15<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834367209\"><div data-type=\"problem\" id=\"fs-id1167834367211\"><span data-type=\"media\" id=\"fs-id1167834367212\" data-alt=\"The figure is a right triangle with sides 16 units and 12 units.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_202_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides 16 units and 12 units.\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834280016\"><div data-type=\"problem\" id=\"fs-id1167834280019\"><span data-type=\"media\" id=\"fs-id1167834280020\" data-alt=\"The figure is a right triangle with sides 15 units and 20 units.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_203_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides 15 units and 20 units.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167834179724\"><p id=\"fs-id1167834179726\">25<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835307426\"><div data-type=\"problem\" id=\"fs-id1167835307428\"><span data-type=\"media\" id=\"fs-id1167835307429\" data-alt=\"The figure is a right triangle with sides 5 units and 12 units.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_204_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides 5 units and 12 units.\"><\/span><\/div><\/div><p id=\"fs-id1167828420159\">In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth if necessary.<\/p><div data-type=\"exercise\" id=\"fs-id1167835274878\"><div data-type=\"problem\" id=\"fs-id1167835274880\"><span data-type=\"media\" id=\"fs-id1167835274881\" data-alt=\"The figure is a right triangle with sides 6 units and 10 units.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_205_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides 6 units and 10 units.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167831836516\"><p id=\"fs-id1167831836518\">8<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167831836523\"><div data-type=\"problem\" id=\"fs-id1167831836526\"><span data-type=\"media\" id=\"fs-id1167831836527\" data-alt=\"The figure is a right triangle with a side that is 9 units and a hypotenuse that is 13 units.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_206_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with a side that is 9 units and a hypotenuse that is 13 units.\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835319680\"><div data-type=\"problem\" id=\"fs-id1167835319682\"><span data-type=\"media\" id=\"fs-id1167835319683\" data-alt=\"The figure is a right triangle with a side that is 5 units and a hypotenuse that is 13 units.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_207_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with a side that is 5 units and a hypotenuse that is 13 units.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167830694080\"><p id=\"fs-id1167830694082\">12<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167830694087\"><div data-type=\"problem\" id=\"fs-id1167830694090\"><span data-type=\"media\" id=\"fs-id1167830694091\" data-alt=\"The figure is a right triangle with a side that is 16 units and a hypotenuse that is 20 units.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_208_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with a side that is 16 units and a hypotenuse that is 20 units.\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832031167\"><div data-type=\"problem\" id=\"fs-id1167832031169\"><span data-type=\"media\" id=\"fs-id1167832031170\" data-alt=\"The figure is a right triangle with a side that is 8 units and a hypotenuse that is 13 units.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_209_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with a side that is 8 units and a hypotenuse that is 13 units.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167835511301\"><p id=\"fs-id1167835511303\">\\(10.2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834505182\"><div data-type=\"problem\" id=\"fs-id1167834505184\"><span data-type=\"media\" id=\"fs-id1167834505186\" data-alt=\"The figure is a right triangle with sides that are both 6 units.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_210_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides that are both 6 units.\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834192417\"><div data-type=\"problem\" id=\"fs-id1167831825080\"><span data-type=\"media\" id=\"fs-id1167831825081\" data-alt=\"The figure is a right triangle with sides that are 5 units and 11 units.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_211_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides that are 5 units and 11 units.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167831825093\"><p id=\"fs-id1167835357419\">\\(9.8\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835357427\"><div data-type=\"problem\" id=\"fs-id1167835357430\"><span data-type=\"media\" id=\"fs-id1167835357431\" data-alt=\"The figure is a right triangle with sides that are 5 units and 7 units.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_212_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides that are 5 units and 7 units.\"><\/span><\/div><\/div><p id=\"fs-id1167835351900\">In the following exercises, solve using a geometry formula.<\/p><div data-type=\"exercise\" id=\"fs-id1167835351903\"><div data-type=\"problem\" id=\"fs-id1167835351905\"><p id=\"fs-id1167835351908\">The width of a rectangle is seven meters less than the length. The perimeter is 58 meters. Find the length and width.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835369827\"><p id=\"fs-id1167835369829\">18 meters, 11 meters<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835369834\"><div data-type=\"problem\" id=\"fs-id1167835369836\"><p id=\"fs-id1167831933905\">The length of a rectangle is eight feet more than the width. The perimeter is 60 feet. Find the length and width.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167831933918\"><div data-type=\"problem\" id=\"fs-id1167826857090\"><p id=\"fs-id1167826857092\">The width of the rectangle is 0.7 meters less than the length. The perimeter of a rectangle is 52.6 meters. Find the dimensions of the rectangle.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167832075583\"><p id=\"fs-id1167832075585\">\\(13.5\\) m, \\(12.8\\) m<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834131256\"><div data-type=\"problem\" id=\"fs-id1167834131258\"><p id=\"fs-id1167834131260\">The length of the rectangle is 1.1 meters less than the width. The perimeter of a rectangle is 49.4 meters. Find the dimensions of the rectangle.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826978925\"><div data-type=\"problem\" id=\"fs-id1167826978927\"><p id=\"fs-id1167835623450\">The perimeter of a rectangle of 150 feet. The length of the rectangle is twice the width. Find the length and width of the rectangle.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835623455\"><p id=\"fs-id1167835623458\">25 ft, 50 ft<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835623463\"><div data-type=\"problem\" id=\"fs-id1167826874392\"><p id=\"fs-id1167826874395\">The length of the rectangle is three times the width. The perimeter of a rectangle is 72 feet. Find the length and width of the rectangle.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835238812\"><div data-type=\"problem\" id=\"fs-id1167835238814\"><p id=\"fs-id1167835238816\">The length of the rectangle is three meters less than twice the width. The perimeter of a rectangle is 36 meters. Find the dimensions of the rectangle.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835238822\"><p id=\"fs-id1167835238824\">7 m, 11 m<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834534825\"><div data-type=\"problem\"><p id=\"fs-id1167834534830\">The length of a rectangle is five inches more than twice the width. The perimeter is 34 inches. Find the length and width.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834098370\"><div data-type=\"problem\" id=\"fs-id1167834098372\"><p id=\"fs-id1167834098375\">The perimeter of a triangle is 39 feet. One side of the triangle is one foot longer than the second side. The third side is two feet longer than the second side. Find the length of each side.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834152069\"><p id=\"fs-id1167834152071\">12 ft, 13 ft, 14 ft<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834152076\"><div data-type=\"problem\" id=\"fs-id1167834152078\"><p id=\"fs-id1167834152080\">The perimeter of a triangle is 35 feet. One side of the triangle is five feet longer than the second side. The third side is three feet longer than the second side. Find the length of each side.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834280036\"><div data-type=\"problem\" id=\"fs-id1167834280039\"><p id=\"fs-id1167826941193\">One side of a triangle is twice the smallest side. The third side is five feet more than the shortest side. The perimeter is 17 feet. Find the lengths of all three sides.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167826941199\"><p id=\"fs-id1167826941201\">3 ft, 6 ft, 8 ft<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826941207\"><div data-type=\"problem\" id=\"fs-id1167834372298\"><p id=\"fs-id1167834372300\">One side of a triangle is three times the smallest side. The third side is three feet more than the shortest side. The perimeter is 13 feet. Find the lengths of all three sides.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167831892734\"><div data-type=\"problem\" id=\"fs-id1167831892736\"><p id=\"fs-id1167831892739\">The perimeter of a rectangular field is 560 yards. The length is 40 yards more than the width. Find the length and width of the field.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167831892744\"><p id=\"fs-id1167831892746\">120 yd, 160 yd<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826994856\"><div data-type=\"problem\" id=\"fs-id1167826994858\"><p id=\"fs-id1167826994860\">The perimeter of a rectangular atrium is 160 feet. The length is 16 feet more than the width. Find the length and width of the atrium.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167831921653\"><div data-type=\"problem\" id=\"fs-id1167831921655\"><p id=\"fs-id1167831921657\">A rectangular parking lot has perimeter 250 feet. The length is five feet more than twice the width. Find the length and width of the parking lot.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167831921663\"><p id=\"fs-id1167834314777\">40 ft, 85 ft<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834314783\"><div data-type=\"problem\" id=\"fs-id1167834314785\"><p id=\"fs-id1167834314787\">A rectangular rug has perimeter 240 inches. The length is 12 inches more than twice the width. Find the length and width of the rug.<\/p><\/div><\/div><p id=\"fs-id1167835301802\">In the following exercises, solve. Approximate answers to the nearest tenth, if necessary.<\/p><div data-type=\"exercise\" id=\"fs-id1167835301805\"><div data-type=\"problem\" id=\"fs-id1167835301807\"><p id=\"fs-id1167835369467\">A 13-foot string of lights will be attached to the top of a 12-foot pole for a holiday display as shown. How far from the base of the pole should the end of the string of lights be anchored?<\/p><span data-type=\"media\" id=\"fs-id1167835369472\" data-alt=\"The figure is an illustration that shows a 13 foot string of lights attached diagonally to the top of a 12 foot pole.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_213_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is an illustration that shows a 13 foot string of lights attached diagonally to the top of a 12 foot pole.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167834526266\"><p id=\"fs-id1167834526268\">5 feet<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834526273\"><div data-type=\"problem\" id=\"fs-id1167834526276\"><p id=\"fs-id1167831883120\">am wants to put a banner across her garage door diagonally, as shown, to congratulate her son for his college graduation. The garage door is 12 feet high and 16 feet wide. Approximately how long should the banner be to fit the garage door?<\/p><span data-type=\"media\" id=\"fs-id1167831883125\" data-alt=\"The figure is an illustration of a banner positioned diagonally across a garage door that is 12 feet high and 16 feet wide.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_214_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is an illustration of a banner positioned diagonally across a garage door that is 12 feet high and 16 feet wide.\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835374354\"><div data-type=\"problem\" id=\"fs-id1167835374356\"><p id=\"fs-id1167831923518\">Chi is planning to put a diagonal path of paving stones through her flower garden as shown. The flower garden is a square with side 10 feet. What will the length of the path be?<\/p><span data-type=\"media\" id=\"fs-id1167831923522\" data-alt=\"The figure is an illustration of a diagonal path of stones through a square garden with 10 foot sides.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_215_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is an illustration of a diagonal path of stones through a square garden with 10 foot sides.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167835328668\"><p id=\"fs-id1167835328670\">14.1 feet<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835328676\"><div data-type=\"problem\" id=\"fs-id1167835328678\"><p id=\"fs-id1167832052679\">Brian borrowed a 20-foot extension ladder to use when he paints his house. If he sets the base of the ladder six feet from the house as shown, how far up will the top of the ladder reach?<\/p><span data-type=\"media\" id=\"fs-id1167832052684\" data-alt=\"The figure is an illustration of a house that has a ladder against it. The ladder is 20 feet. Its base is positioned 6 feet from the house.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_216_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is an illustration of a house that has a ladder against it. The ladder is 20 feet. Its base is positioned 6 feet from the house.\"><\/span><\/div><\/div><\/div><div class=\"everyday\" data-depth=\"2\" id=\"fs-id1167835595163\"><h4 data-type=\"title\">Everyday Math<\/h4><div data-type=\"exercise\" id=\"fs-id1167835513249\"><div data-type=\"problem\" id=\"fs-id1167835513251\"><p id=\"fs-id1167835513253\"><strong data-effect=\"bold\">Converting temperature<\/strong> While on a tour in Greece, Tatyana saw that the temperature was 40\u00b0 Celsius. Solve for <em data-effect=\"italics\">F<\/em> in the formula \\(C=\\frac{5}{9}\\left(F-32\\right)\\) to find the Fahrenheit temperature.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167827940346\"><p id=\"fs-id1167827940349\">\\(104\\text{\u00b0}\\phantom{\\rule{0.2em}{0ex}}\\text{F}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835640088\"><div data-type=\"problem\" id=\"fs-id1167835640090\"><p id=\"fs-id1167835640092\"><strong data-effect=\"bold\">Converting temperature<\/strong> Yon was visiting the United States and he saw that the temperature in Seattle one day was 50\u00b0 Fahrenheit. Solve for <em data-effect=\"italics\">C<\/em> in the formula \\(F=\\frac{9}{5}C+32\\) to find the Celsius temperature.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834396122\"><div data-type=\"problem\" id=\"fs-id1167834396124\"><p id=\"fs-id1167834396126\">Christa wants to put a fence around her triangular flowerbed. The sides of the flowerbed are six feet, eight feet and 10 feet. How many feet of fencing will she need to enclose her flowerbed?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834396132\"><p id=\"fs-id1167834396134\">24 ft<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834536483\"><div data-type=\"problem\" id=\"fs-id1167834536485\"><p id=\"fs-id1167834536487\">Jose just removed the children\u2019s play set from his back yard to make room for a rectangular garden. He wants to put a fence around the garden to keep the dog out. He has a 50-foot roll of fence in his garage that he plans to use. To fit in the backyard, the width of the garden must be 10 feet. How long can he make the other side?<\/p><\/div><\/div><\/div><div class=\"writing\" data-depth=\"2\" id=\"fs-id1167834536491\"><h4 data-type=\"title\">Writing Exercises<\/h4><div data-type=\"exercise\" id=\"fs-id1167834527706\"><div data-type=\"problem\" id=\"fs-id1167834527708\"><p id=\"fs-id1167834527710\">If you need to put tile on your kitchen floor, do you need to know the perimeter or the area of the kitchen? Explain your reasoning.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834527715\"><p id=\"fs-id1167830960523\">Answers will vary.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167830960528\"><div data-type=\"problem\" id=\"fs-id1167830960530\"><p id=\"fs-id1167830960532\">If you need to put a fence around your backyard, do you need to know the perimeter or the area of the backyard? Explain your reasoning.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835410188\"><div data-type=\"problem\" id=\"fs-id1167835410190\"><p id=\"fs-id1167835410192\">Look at the two figures below.<\/p><span data-type=\"media\" id=\"fs-id1167834464375\" data-alt=\"A figure of a rectangle with a width that is 2 units and a length that is 8 units and a square with sides that are 4 units.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_217_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"A figure of a rectangle with a width that is 2 units and a length that is 8 units and a square with sides that are 4 units.\"><\/span><p id=\"fs-id1167834464388\"><span class=\"token\">\u24d0<\/span> Which figure looks like it has the larger area? Which looks like it has the larger perimeter?<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> Now calculate the area and perimeter of each figure. Which has the larger area? Which has the larger perimeter?<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span> Were the results of part (b) the same as your answers in part (a)? Is that surprising to you?<\/div><div data-type=\"solution\" id=\"fs-id1167835498857\"><p id=\"fs-id1167835498859\"><span class=\"token\">\u24d0<\/span> Answers will vary. <span class=\"token\">\u24d1<\/span> The areas are the same. The \\(2\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}8\\) rectangle has a larger perimeter than the \\(4\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}4\\) square.<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span> Answers will vary.<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835488632\"><div data-type=\"problem\" id=\"fs-id1167835488634\"><p id=\"fs-id1167835488636\">Write a geometry word problem that relates to your life experience, then solve it and explain all your steps.<\/p><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167831920420\"><h4 data-type=\"title\">Self Check<\/h4><p id=\"fs-id1167831920426\"><span class=\"token\">\u24d0<\/span> After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p><span data-type=\"media\" id=\"fs-id1167834517528\" data-alt=\"This table has four columns and three rows. The first row is a header and it labels each column, \u201cI can\u2026\u201d, \u201cConfidently,\u201d \u201cWith some help,\u201d and \u201cNo-I don\u2019t get it!\u201d In row 2, the I can was solve a formula for a specific variable. In row 3, the I can was use formulas to solve geometry applications.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_218_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This table has four columns and three rows. The first row is a header and it labels each column, \u201cI can\u2026\u201d, \u201cConfidently,\u201d \u201cWith some help,\u201d and \u201cNo-I don\u2019t get it!\u201d In row 2, the I can was solve a formula for a specific variable. In row 3, the I can was use formulas to solve geometry applications.\"><\/span><p id=\"fs-id1167835375366\"><span class=\"token\">\u24d1<\/span> What does this checklist tell you about your mastery of this section? What steps will you take to improve?<\/p><\/div><\/div>\n","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<p>By the end of this section, you will be able to: <\/p>\n<ul>\n<li>Solve a formula for a specific variable<\/li>\n<li>Use formulas to solve geometry applications<\/li>\n<\/ul>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167830838404\" class=\"be-prepared\">\n<p id=\"fs-id1167826829110\">Before you get started, take this readiness quiz.<\/p>\n<ol id=\"fs-id1167835375034\" type=\"1\">\n<li>Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-bd80e1fac6f93bb7b90caf3ba4bc2327_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-293cae06997efc99f11b7f0e51bfa8ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"47\" style=\"vertical-align: 0px;\" \/>\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/d3697553-3900-453f-8c08-8f74d55711ba#fs-id1167836530265\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<li>The length of a rectangle is three less than the width. Let <em data-effect=\"italics\">w<\/em> represent the width. Write an expression for the length of the rectangle.\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/d3697553-3900-453f-8c08-8f74d55711ba#fs-id1167836606933\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<li>Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3c65f514d7fad4f3e5b7763e8019b4e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"27\" style=\"vertical-align: -6px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ee951a7e5630634730f11f6c2ab8ccc9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#61;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"49\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-355cd69b55bf1a11db0b337f05984d86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#61;&#57;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"47\" style=\"vertical-align: 0px;\" \/>\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/425620d9-51dd-45e5-8a21-953998a4a77f#fs-id1167829754333\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<\/ol>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167830979736\">\n<h3 data-type=\"title\">Solve a Formula for a Specific Variable<\/h3>\n<p id=\"fs-id1167835509982\">We have all probably worked with some geometric formulas in our study of mathematics. Formulas are used in so many fields, it is important to recognize formulas and be able to manipulate them easily.<\/p>\n<p id=\"fs-id1167830866056\">It is often helpful to solve a formula for a specific variable. If you need to put a formula in a spreadsheet, it is not unusual to have to solve it for a specific variable first. We isolate that variable on one side of the equals sign with a coefficient of one and all other variables and constants are on the other side of the equal sign.<\/p>\n<p id=\"fs-id1167834538150\">Geometric formulas often need to be solved for another variable, too. The formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d667667489cc5c52babfc35a69f51ee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"86\" style=\"vertical-align: -6px;\" \/> is used to find the <span data-type=\"term\" class=\"no-emphasis\">volume<\/span> of a right circular cone when given the radius of the base and height. In the next example, we will solve this formula for the height.<\/p>\n<div data-type=\"example\" id=\"fs-id1167835351780\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167832015818\">\n<div data-type=\"problem\" id=\"fs-id1167831116495\">\n<p id=\"fs-id1167834515411\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d667667489cc5c52babfc35a69f51ee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"86\" style=\"vertical-align: -6px;\" \/> for <em data-effect=\"italics\">h<\/em>.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167831872111\">\n<table id=\"fs-id1167828349231\" class=\"unnumbered unstyled\" summary=\"Write the formula. It is V is equal to one-third times pi times r squared times h. Clear the fractions by multiplying each side by 3. The result is 3 times V is equal to 3 times third times pi times r squared times h. Simplify. The result is 3 V is equal to pi times r squared times h. Divide both sides by pi times r squared. The result is 3 V divided by pi times r squared is equal to h.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Write the formula.<\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835595188\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_001a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Remove the fraction on the right.<\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167834423545\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_001b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Simplify.<\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835325472\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_001c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Divide both sides by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-95c700b05c62c86a1d1200b4688f17e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167831913473\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_001d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1167835377710\">We could now use this formula to find the height of a right circular cone when we know the volume and the radius of the base, by using the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ec7847b6a2795d70ed379bbe803f1825_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#86;&#125;&#123;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"63\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167826937766\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167835237040\">\n<div data-type=\"problem\" id=\"fs-id1167831893290\">\n<p id=\"fs-id1167835310695\">Use the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b372c8f17c232fb83c5e06a24bf6fd73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/> to solve for <em data-effect=\"italics\">b<\/em>.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835356655\">\n<p id=\"fs-id1167834340022\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a0d9397e145e622bd2b77dc4fdb9d7a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#65;&#125;&#123;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"51\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167831106692\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167835509131\">\n<div data-type=\"problem\" id=\"fs-id1167835354790\">\n<p id=\"fs-id1167835378068\">Use the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b372c8f17c232fb83c5e06a24bf6fd73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/> to solve for <em data-effect=\"italics\">h<\/em>.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167831825126\">\n<p id=\"fs-id1167830697638\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b38e963988a711953aacc45c0687c2cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#65;&#125;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"54\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167835302021\">In the sciences, we often need to change <span data-type=\"term\" class=\"no-emphasis\">temperature<\/span> from Fahrenheit to Celsius or vice versa. If you travel in a foreign country, you may want to change the Celsius temperature to the more familiar Fahrenheit temperature.<\/p>\n<div data-type=\"example\" id=\"fs-id1167835303530\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167835358195\">\n<div data-type=\"problem\" id=\"fs-id1167834063520\">\n<p id=\"fs-id1167831826403\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-827f8035affe1c5d4cfd48235dc2918d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#57;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#70;&#45;&#51;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"118\" style=\"vertical-align: -6px;\" \/> for <em data-effect=\"italics\">F<\/em>.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835284989\">\n<table id=\"fs-id1167832054604\" class=\"unnumbered unstyled\" summary=\"Write the formula. It is C is equal to five-ninths times the quantity F minus 32. Clear the fractions by multiplying each side by nine-fifths C is equal to nine-fifths time s five-ninths times the quantity F minus 32. Simplify. The result is nine-fifths C is equal to F minus 32. Add 32 to both sides. The result is nine-fifths C plus 32 is equal to F. We can now use the formula F is equal to nine-fifths C plus 32 to find the Fahrenheit temperature when we know the Celsius.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Write the formula.<\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167834063097\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_002a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Remove the fraction on the right.<\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835192392\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_002b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Simplify.<\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167834130526\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_002c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Add 32 to both sides.<\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835421279\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_002d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1167831106790\">We can now use the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0eae5cacfec517ea5c3fe4b03a538cd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#53;&#125;&#67;&#43;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"101\" style=\"vertical-align: -6px;\" \/> to find the Fahrenheit temperature when we know the Celsius temperature.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167835377185\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167835303972\">\n<div data-type=\"problem\" id=\"fs-id1167831832047\">\n<p id=\"fs-id1167835380142\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0eae5cacfec517ea5c3fe4b03a538cd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#53;&#125;&#67;&#43;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"101\" style=\"vertical-align: -6px;\" \/> for <em data-effect=\"italics\">C<\/em>.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835311501\">\n<p id=\"fs-id1167835534081\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-827f8035affe1c5d4cfd48235dc2918d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#57;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#70;&#45;&#51;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"118\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167835369511\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167835381542\">\n<div data-type=\"problem\" id=\"fs-id1167835304190\">\n<p id=\"fs-id1167834429234\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2ba043180b8e6deacd10152d0555e56f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#66;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"117\" style=\"vertical-align: -6px;\" \/> for <em data-effect=\"italics\">b<\/em>.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835358252\">\n<p id=\"fs-id1167835362584\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-548dd441ce5afc4fabbb7fe7f3b6c220_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#65;&#45;&#66;&#104;&#125;&#123;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"80\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167835336973\">The next example uses the formula for the <span data-type=\"term\" class=\"no-emphasis\">surface area<\/span> of a right cylinder.<\/p>\n<div data-type=\"example\" id=\"fs-id1167835308479\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167835334948\">\n<div data-type=\"problem\" id=\"fs-id1167831107017\">\n<p id=\"fs-id1167834185892\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7238ac6acdb23124ab4cff2dc10d4313_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#50;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#92;&#112;&#105;&#32;&#114;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"131\" style=\"vertical-align: -2px;\" \/> for <em data-effect=\"italics\">h<\/em>.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835326559\">\n<table id=\"fs-id1167835609380\" class=\"unnumbered unstyled\" summary=\"Write the formula. It is S is equal to 2 times pi times r squared plus 2 times pi times r times h. Isolate the h term by subtracting 2 times pi times r squared from each side. Simplify. The result is S minus 2 times pi times r squared is equal to 2 times pi times r times h. Solve for h by dividing both sides by 2 times pi times r. The quotient of the quantity S minus 2 times pi times r squared and 2 times pi times r is equal to the quotient of 2 times pi times r times h and 2 times pi times r. Simplify. The result is the quotient of the quantity S minus 2 times pi times r squared and 2 times pi times r is equal to h.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Write the formula.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167834539276\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_003a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Isolate the <em data-effect=\"italics\">h<\/em> term by subtracting <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-091b174958cb21a7f7c732fada81c3e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: 0px;\" \/> from each side.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835332492\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_003b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Simplify.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167831832980\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_003c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Solve for <em data-effect=\"italics\">h<\/em> by dividing both sides by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a1df89ff2f5b8fa4814fd85eab8a197c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#112;&#105;&#32;&#114;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835321840\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_003d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Simplify.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835338667\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_003e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167830693722\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167835367654\">\n<div data-type=\"problem\" id=\"fs-id1167835639920\">\n<p id=\"fs-id1167832054166\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cb2b959075a35b22d27a26a2141b3f5e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#80;&#43;&#80;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"101\" style=\"vertical-align: -2px;\" \/> for <em data-effect=\"italics\">t<\/em>.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167832056441\">\n<p id=\"fs-id1167835307993\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ad2e37b86d7621af94dd7e39a6dca4c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#65;&#45;&#80;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#125;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"64\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167834301254\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167835214381\">\n<div data-type=\"problem\" id=\"fs-id1167834195235\">\n<p id=\"fs-id1167835356631\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cb2b959075a35b22d27a26a2141b3f5e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#80;&#43;&#80;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"101\" style=\"vertical-align: -2px;\" \/> for <em data-effect=\"italics\">r<\/em>.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835344198\">\n<p id=\"fs-id1167831883053\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-59658a97f798a82be26b2f689ebab220_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#65;&#45;&#80;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#125;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167835375360\">Sometimes we might be given an equation that is solved for <em data-effect=\"italics\">y<\/em> and need to solve it for <em data-effect=\"italics\">x<\/em>, or vice versa. In the following example, we\u2019re given an equation with both <em data-effect=\"italics\">x<\/em> and <em data-effect=\"italics\">y<\/em> on the same side and we\u2019ll solve it for <em data-effect=\"italics\">y<\/em>.<\/p>\n<div data-type=\"example\" id=\"fs-id1167835229496\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167826869989\">\n<div data-type=\"problem\" id=\"fs-id1167835309130\">\n<p id=\"fs-id1167835390378\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6f466b92f218bb70eaf7398ba7694189_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#43;&#55;&#121;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"99\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y<\/em>.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835327650\">\n<table id=\"fs-id1167834184073\" class=\"unnumbered unstyled\" summary=\"We will isolate y on one side of the equation, 8 x plus 7 y is equal to 15. Subtract 6 x from both sides to isolate the term with y. 8 x minus 8 x plus 7 y is equal to 15 minus 8 x. Simplify. The result is 7 y is equal to 15 minus 8 x. Divided both sides y 7 to make the coefficient of y 1. 7 y divided by 7 is equal to the quantity 15 minus 8 x divided y 7. Simplify. The result is y is equal to the quantity 15 minus 8 x all divided by 7.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">We will isolate <em data-effect=\"italics\">y<\/em> on one side of the equation.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835205571\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_004a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9dbdb28b1297d32a21861bc74971aeae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/> from both sides to isolate the term with <em data-effect=\"italics\">y<\/em>.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835376882\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_004b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Simplify.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167834195971\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_004c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Divide both sides by 7 to make the coefficient of <em data-effect=\"italics\">y<\/em> one.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835347694\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_004d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Simplify.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835240731\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_004e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167830963131\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167835267517\">\n<div data-type=\"problem\" id=\"fs-id1167835238140\">\n<p id=\"fs-id1167835225799\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-388a3aebe8ce00f8ea4870c4c9b64099_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#55;&#121;&#61;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"91\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y<\/em>.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167826987940\">\n<p id=\"fs-id1167834489799\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6f8352d5341e24907144f8cc52dcf354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#45;&#52;&#120;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167835229662\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167835303350\">\n<div data-type=\"problem\" id=\"fs-id1167835343793\">\n<p id=\"fs-id1167835358951\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-63b0896e57119239d954331b44213d02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#43;&#56;&#121;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"90\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y<\/em>.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835254555\">\n<p id=\"fs-id1167834489871\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ce6d0502e49bccea8c078681d0d5acb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#45;&#53;&#120;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167835417752\">\n<h3 data-type=\"title\">Use Formulas to Solve Geometry Applications<\/h3>\n<p>In this objective we will use some common geometry formulas. We will adapt our problem solving strategy so that we can solve geometry applications. The geometry formula will name the variables and give us the equation to solve.<\/p>\n<p id=\"fs-id1167835190527\">In addition, since these applications will all involve shapes of some sort, most people find it helpful to draw a figure and label it with the given information. We will include this in the first step of the problem solving strategy for geometry applications.<\/p>\n<div data-type=\"note\" id=\"fs-id1167830960720\" class=\"howto\">\n<div data-type=\"title\">Solve geometry applications.<\/div>\n<ol id=\"fs-id1167834395861\" type=\"1\" class=\"stepwise\">\n<li><strong data-effect=\"bold\">Read<\/strong> the problem and make sure all the words and ideas are understood.<\/li>\n<li><strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/li>\n<li><strong data-effect=\"bold\">Name<\/strong> what we are looking for by choosing a variable to represent it. Draw the figure and label it with the given information.<\/li>\n<li><strong data-effect=\"bold\">Translate<\/strong> into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.<\/li>\n<li><strong data-effect=\"bold\">Solve<\/strong> the equation using good algebra techniques.<\/li>\n<li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem and make sure it makes sense.<\/li>\n<li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li>\n<\/ol>\n<\/div>\n<p id=\"fs-id1167834191598\">When we solve geometry applications, we often have to use some of the properties of the figures. We will review those properties as needed.<\/p>\n<p id=\"fs-id1167834537836\">The next example involves the <span data-type=\"term\" class=\"no-emphasis\">area<\/span> of a triangle. The area of a triangle is one-half the base times the height. We can write this as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d480cad9772d19b2a31d758aa22cbb36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#98;&#104;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"70\" style=\"vertical-align: -6px;\" \/> where <em data-effect=\"italics\">b<\/em> = length of the base and <em data-effect=\"italics\">h<\/em> = height.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167835280765\" data-alt=\"The figure is a triangle with its height shown. Its base is b and its height is h. The formula for the area of the triangle is A is equal to one-half times b times h.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_005_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a triangle with its height shown. Its base is b and its height is h. The formula for the area of the triangle is A is equal to one-half times b times h.\" \/><\/span><\/p>\n<div data-type=\"example\" id=\"fs-id1167832053508\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167835498231\">\n<div data-type=\"problem\" id=\"fs-id1167835324990\">\n<p id=\"fs-id1167835310355\">The area of a triangular painting is 126 square inches. The base is 18 inches. What is the height?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834246972\">\n<table id=\"fs-id1167832151328\" class=\"unnumbered unstyled\" summary=\"Step 1 is to read the problem. Step 2 is to identify what you are looking for. It is the height of a triangle. Step 3 is to name the height. Choose a variable to represent it. Let h be the height. Draw the figure and label it with the given information. The area is 126 square inches. The height is h and the base is 18 inches. Step 4 is to translate. Write the appropriate formula. It is A is equal to one-half times b times h. Substitute in the given information. 126 is equal to one-half times 18 times h. Step 5 is to solve the equation. 126 is equal to 9 h. Divide both sides by 9. 14 is equal h. Step 6 is to check using A is equal to one-half b times h. Is 126 equal to one-half times 18 times 14? 126 is equal to 126. The solution checks. Step 7 is to answer the question. The height of the triangle is 14 inches.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for.<\/td>\n<td data-valign=\"top\" data-align=\"left\">height of a triangle<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name.<\/strong><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Choose a variable to represent it.<\/td>\n<td data-valign=\"top\" data-align=\"left\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-62bcd55cff5bacf6b29f3badcbd52342_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"28\" style=\"vertical-align: 0px;\" \/> the height.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Draw the figure and label it with the given information.<\/td>\n<td data-valign=\"top\" data-align=\"left\">Area = 126 sq. in.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835358741\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_006a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate.<\/strong><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Write the appropriate formula.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-10131d6872781ef84903f58cbe71e76f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#56;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Substitute in the given information.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e0efcf1ebf253cd864ff97670ba6c306_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#50;&#54;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&middot;&#49;&#56;&middot;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"88\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-58203f2214ef54f18a4b099253636ce0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#50;&#54;&#61;&#57;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"68\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Divide both sides by 9.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a4cfae07f1160b0abccd2baf8497987b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#52;&#61;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"50\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check<\/strong>.<\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6a0445c0ffb46f3c5b6279e2eddfb13e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#65;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#98;&#104;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#50;&#54;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&middot;&#49;&#56;&middot;&#49;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#50;&#54;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#49;&#50;&#54;&#10003;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"67\" width=\"119\" style=\"vertical-align: -26px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td>\n<td data-valign=\"top\" data-align=\"left\">The height of the triangle is 14 inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167835333601\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167831872255\">\n<div data-type=\"problem\" id=\"fs-id1167834098416\">\n<p id=\"fs-id1167828434993\">The area of a triangular church window is 90 square meters. The base of the window is 15 meters. What is the window\u2019s height?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835339652\">\n<p id=\"fs-id1167826994288\">The window\u2019s height is 12 meters.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167835308936\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167835210509\">\n<div data-type=\"problem\" id=\"fs-id1167831871573\">\n<p id=\"fs-id1167835359458\">A triangular tent door has area 15 square feet. The height is five feet. What is the length of the base?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835595818\">\n<p id=\"fs-id1167832058183\">The length of the base is 6 feet.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167831076560\">In the next example, we will work with a <span data-type=\"term\" class=\"no-emphasis\">right triangle<\/span>. To solve for the measure of each angle, we need to use two triangle properties. In any triangle, the sum of the measures of the angles is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0a5f5a152c93587da38d3600cbc59428_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&deg;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/> We can write this as a formula: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-440d5edfd835b36ad954e5dc0cff8fe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#92;&#97;&#110;&#103;&#108;&#101;&#32;&#65;&#43;&#109;&#92;&#97;&#110;&#103;&#108;&#101;&#32;&#66;&#43;&#109;&#92;&#97;&#110;&#103;&#108;&#101;&#32;&#67;&#61;&#49;&#56;&#48;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"225\" style=\"vertical-align: -2px;\" \/> Also, since the triangle is a right triangle, we remember that a right triangle has one <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ad7fa5a1576b957af1a577f736d676e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&deg;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> angle.<\/p>\n<p id=\"fs-id1167834472483\">Here, we will have to define one angle in terms of another. We will wait to draw the figure until we write expressions for all the angles we are looking for.<\/p>\n<div data-type=\"example\" id=\"fs-id1167835349183\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167835514607\">\n<div data-type=\"problem\" id=\"fs-id1167832058290\">\n<p id=\"fs-id1167835343222\">The measure of one angle of a right triangle is 40 degrees more than the measure of the smallest angle. Find the measures of all three angles.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835181009\">\n<table id=\"fs-id1167828420750\" class=\"unnumbered unstyled\" summary=\"Step 1 is to read the problem. Step 2 is to identify what you are looking for. It is the measures of all three angles. Step 3 is to name the variable to represent it. Let a be equal to the first angle, a plus 40 be equal to the second angle, and 90 be equal to the third angle, or the right angle. Draw the figure and label it with the given information. The figure is the triangle A B C, with A measuring a plus 40, B measuring a, and C measuring 90. Step 4 is to translate. Write the appropriate formula. The measure of A plus the measure of B plus the measure of C is equal to 180. Substitute into the formula. The result is a plus the quantity a plus 40 plus 90 is equal to 180. Step 5 is to solve the equation. 2 a plus 130 is equal to 180. 2 a is equal to 50, which is the first angle. a plus 20 is the second angle. 25 plus 20 is 45. 90 is the third angle. Step 6 is to check the solutions. Is 25 plus 45 plus 90 is equal to 180? 180 is equal to 180. The solutions check. Step 7 is to answer the question. The three angles measure 25 degrees, 45 degrees, and 90 degrees.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for.<\/td>\n<td data-valign=\"top\" data-align=\"left\">the measures of all three angles<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name.<\/strong> Choose a variable to represent it.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a20b58da9ed590dd6e1dc3129fa9ef85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#76;&#101;&#116;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#123;&#49;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#116;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#103;&#108;&#101;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#43;&#52;&#48;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#123;&#50;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#103;&#108;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#57;&#48;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#123;&#51;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#103;&#108;&#101;&#32;&#40;&#116;&#104;&#101;&#32;&#114;&#105;&#103;&#104;&#116;&#32;&#97;&#110;&#103;&#108;&#101;&#41;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"295\" style=\"vertical-align: -26px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Draw the figure and label it with the given information.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835355270\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_007a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate.<\/strong><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Write the appropriate formula.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167831086842\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_007b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Substitute into the formula.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835512003\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_007c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167834309725\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_007d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check<\/strong>.<\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9b0b01e0a07ba3c2e2af8346ea35777d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#53;&#43;&#54;&#53;&#43;&#57;&#48;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#49;&#56;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#56;&#48;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#49;&#56;&#48;&#10003;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"170\" style=\"vertical-align: -15px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td>\n<td data-valign=\"top\" data-align=\"left\">The three angles measure <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c60f14fe7ae8e379404714f3c9eb1d22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#92;&#116;&#101;&#120;&#116;&#123;&deg;&#125;&#44;&#54;&#53;&#92;&#116;&#101;&#120;&#116;&#123;&deg;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"48\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-86180b1e44fdf01ec55baa94a830a4ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&deg;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167834279890\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167835310675\">\n<div data-type=\"problem\" id=\"fs-id1167835342932\">\n<p id=\"fs-id1167834193267\">The measure of one angle of a right triangle is 50 more than the measure of the smallest angle. Find the measures of all three angles.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167826996842\">\n<p id=\"fs-id1167835232400\">The measures of the angles are 20\u00b0, 70\u00b0, and 90\u00b0.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167826967450\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167835329250\">\n<div data-type=\"problem\" id=\"fs-id1167834505390\">\n<p id=\"fs-id1167835330290\">The measure of one angle of a right triangle is 30 more than the measure of the smallest angle. Find the measures of all three angles.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835320678\">\n<p id=\"fs-id1167835231754\">The measures of the angles are 30\u00b0, 60\u00b0, and 90\u00b0.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167835337264\">The next example uses another important geometry formula. The <span data-type=\"term\">Pythagorean Theorem<\/span> tells how the lengths of the three sides of a right triangle relate to each other. Writing the formula in every exercise and saying it aloud as you write it may help you memorize the Pythagorean Theorem.<\/p>\n<div data-type=\"note\" id=\"fs-id1167834185486\">\n<div data-type=\"title\">The Pythagorean Theorem<\/div>\n<p id=\"fs-id1167835238717\">In any right triangle, where <em data-effect=\"italics\">a<\/em> and <em data-effect=\"italics\">b<\/em> are the lengths of the legs, and <em data-effect=\"italics\">c<\/em> is the length of the hypotenuse, the sum of the squares of the lengths of the two legs equals the square of the length of the hypotenuse.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167835328326\" data-alt=\"The figure is a right triangle with sides a and b, and a hypotenuse c. a squared plus b squared is equal to c squared. In a right triangle, the sum of the squares of the lengths of the two legs equals the square of the length of the hypotenuse.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_008_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides a and b, and a hypotenuse c. a squared plus b squared is equal to c squared. In a right triangle, the sum of the squares of the lengths of the two legs equals the square of the length of the hypotenuse.\" \/><\/span><\/div>\n<p id=\"fs-id1167835267622\">We will use the Pythagorean Theorem in the next example.<\/p>\n<div data-type=\"example\" id=\"fs-id1167832054640\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167835299766\">\n<div data-type=\"problem\" id=\"fs-id1167835356454\">\n<p id=\"fs-id1167831117359\">Use the Pythagorean Theorem to find the length of the other leg in<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167832074734\" data-alt=\"This figure is a right triangle with one leg that is 12 units and a hypotenuse that is 13 units.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_009_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure is a right triangle with one leg that is 12 units and a hypotenuse that is 13 units.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167835215305\">\n<table id=\"fs-id1167835233076\" class=\"unnumbered unstyled can-break\" summary=\"Step 1 is to read the problem. Step 2 is to identify what you are looking for. We are looking for the leg of the triangle. Step is to name a variable to represent it. Let a be equal to the leg of the triangle. Label side a. Now the figure is a right triangle with one leg that is 12 units, one leg that is a, and a hypotenuse that is 13 units. Step 4 is to translate. Write the appropriate formula, a squared plus b squared is equal to c squared. Substitute, so a squared plus 12 squared is equal to 13 squared. Step 5 is to solve the equation, a squared plus 144 is equal to 169. Isolate the variable term. The result is a squared is equal to 25. Use the definition of the square root. The result is a is equal to the square root of 25. Simplify. The result is a is equal to 25. Step 6 is to check the answer. Is 5 squared plus 12 squared is equal to 13 squared? Is 25 plus 144 equal to 169? 169 is equal to 169. The solution checks. Step 7 is to answer the question. The length of the leg is 5 units.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for.<\/td>\n<td data-valign=\"top\" data-align=\"left\">the length of the leg of the triangle<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name.<\/strong><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Choose a variable to represent it.<\/td>\n<td data-valign=\"top\" data-align=\"left\">Let <em data-effect=\"italics\">a<\/em> = the leg of the triangle.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Label side <em data-effect=\"italics\">a<\/em>.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167834448625\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_010b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate.<\/strong><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Write the appropriate formula.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Substitute.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3c2d228943870bcfc94566f8684b649f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#49;&#50;&#125;&#94;&#123;&#50;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#123;&#49;&#51;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"135\" style=\"vertical-align: -13px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Isolate the variable term.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Use the definition of square root.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Simplify.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7b26d45e88e408145d178792ef860e69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#49;&#52;&#52;&#125;&#94;&#123;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#49;&#54;&#57;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#50;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#53;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"82\" width=\"145\" style=\"vertical-align: -33px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check.<\/strong><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167835229462\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_010a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td>\n<td data-valign=\"top\" data-align=\"left\">The length of the leg is 5.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167835306569\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167826814080\">\n<div data-type=\"problem\" id=\"fs-id1167835341581\">\n<p id=\"fs-id1167835348472\">Use the Pythagorean Theorem to find the length of the leg in the figure.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167834473441\" data-alt=\"The figure is a right triangle with legs that are b units and 15 units, and a hypotenuse that is 17 units.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_011_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with legs that are b units and 15 units, and a hypotenuse that is 17 units.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167835343025\">\n<p id=\"fs-id1167835324947\">The length of the leg is 8.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167831871406\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167835335026\">\n<div data-type=\"problem\" id=\"fs-id1167835305859\">\n<p id=\"fs-id1167832134180\">Use the Pythagorean Theorem to find the length of the leg in the figure.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167835189258\" data-alt=\"The figure is a right triangle with legs that are b units and 9 units, and a hypotenuse that is 15 units.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_012_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with legs that are b units and 9 units, and a hypotenuse that is 15 units.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167835380332\">\n<p id=\"fs-id1167831923652\">The length of the leg is 12.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167835305798\">The next example is about the <span data-type=\"term\" class=\"no-emphasis\">perimeter<\/span> of a rectangle. Since the perimeter is just the distance around the rectangle, we find the sum of the lengths of its four sides\u2014the sum of two lengths and two widths. We can write is as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fd41d005b7610a456dc9e5dc6ad9fd67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#50;&#76;&#43;&#50;&#87;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"108\" style=\"vertical-align: -2px;\" \/> where <em data-effect=\"italics\">L<\/em> is the length and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4caed22919a1780df1b6310b338b904e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#87;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/> is the width. To solve the example, we will need to define the length in terms of the width.<\/p>\n<div data-type=\"example\" id=\"fs-id1167834228085\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167828447182\">\n<div data-type=\"problem\" id=\"fs-id1167831116214\">\n<p id=\"fs-id1167835363342\">The length of a rectangle is six centimeters more than twice the width. The perimeter is 96 centimeters. Find the length and width.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834396437\">\n<table id=\"fs-id1167826857370\" class=\"unnumbered unstyled can-break\" summary=\"Step 1 is to read the problem. Step is to identify what we are looking for. We are looking for the length and width. Step 3 is to name the variable to represent the width, Let w be equal to the width. The length is six more than twice the width. So the expression 2 w plus 6 is equal to length. The figure is a rectangle with the width labeled w, a length labeled 2 w plus 6, and the perimeter labeled P is equal to 96 centimeters. Step 4 is to translate. Write the appropriate formula, P is equal to 2 L plus 2 W. Substitute in the given information. 96 is equal to the sum of 2 times the quantity 2 w plus 6 and 2 w. Step 5 is to solve the equation, 96 is equal to 4 w plus 12 plus 2 w. 96 is equal to 6 w plus 12. 84 is equal to 6 w. 14 is equal w, which is the width. 2 w plus 6 represents the length, so 2 times 14 plus 6 is 34. The length is 34 centimeters. Step 6 is to check the answers. The figure is a rectangle with its width labeled 14 centimeters and its length labeled 34 centimeters. The perimeter is given by P is equal to 2 L plus 2 W. Is 96 equal to 2 times 34 plus 2 times 14. 96 is equal to 96, so the answers check. Step 7 is to answer the question. The length is 34 centimeters and the width is 14 centimeters.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td data-valign=\"top\" data-align=\"left\">the length and the width<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name<\/strong>. Choose a variable to represent the width.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> The length is six more than twice the width.<\/td>\n<td data-valign=\"top\" data-align=\"left\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-222a0d9f7ca57c117fe41ab5b1f78938_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#119;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"31\" style=\"vertical-align: 0px;\" \/> width.<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f9cf7910256e3b4ded63f81bfbf595e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#119;&#43;&#54;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"70\" style=\"vertical-align: -2px;\" \/> length<\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167835262242\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_013b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-48c643d6aa94ed9d67859496a0e0b8be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#57;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"55\" style=\"vertical-align: 0px;\" \/> cm<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate.<\/strong><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Write the appropriate formula.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835361664\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_013c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Substitute in the given information.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167834300693\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_013d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve the equation.<\/strong><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167834213903\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_013e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6.<\/strong> Check.<\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167835194800\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_013a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-33d546b4cbb2c7e44c9cf0589c12440c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#80;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#50;&#76;&#43;&#50;&#87;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#57;&#54;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#50;&middot;&#51;&#52;&#43;&#50;&middot;&#49;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#57;&#54;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#57;&#54;&#10003;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"139\" style=\"vertical-align: -25px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer the question.<\/strong><\/td>\n<td data-valign=\"top\" data-align=\"left\">The length is 34 cm and the width is 14 cm.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167835363670\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167831887552\">\n<div data-type=\"problem\" id=\"fs-id1167831887554\">\n<p id=\"fs-id1167834062321\">The length of a rectangle is seven more than twice the width. The perimeter is 110 inches. Find the length and width.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835416847\">\n<p id=\"fs-id1167834536082\">The length is 16 inches and the width is 39 inches.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167834459097\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167835343966\">\n<div data-type=\"problem\" id=\"fs-id1167835343968\">\n<p id=\"fs-id1167835479496\">The width of a rectangle is eight yards less than twice the length. The perimeter is 86 yards. Find the length and width.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835414655\">\n<p id=\"fs-id1167835334484\">The length is 17 yards and the width is 26 yards.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167835343328\">The next example is about the <span data-type=\"term\" class=\"no-emphasis\">perimeter<\/span> of a triangle. Since the perimeter is just the distance around the triangle, we find the sum of the lengths of its three sides. We can write this as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-59bc412fd05b25de9bb75ec2a25b825e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#97;&#43;&#98;&#43;&#99;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"110\" style=\"vertical-align: -4px;\" \/> where <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em> are the lengths of the sides.<\/p>\n<div data-type=\"example\" id=\"fs-id1167835280638\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167835280640\">\n<div data-type=\"problem\" id=\"fs-id1167831895002\">\n<p id=\"fs-id1167831895004\">One side of a triangle is three inches more than the first side. The third side is two inches more than twice the first. The perimeter is 29 inches. Find the length of the three sides of the triangle.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834190033\">\n<table id=\"fs-id1167832043286\" class=\"unnumbered unstyled can-break\" summary=\"Step 1 is to read the problem. Step 2 is to identify what we are looking for. We are looking for the lengths of three sides of a triangle. Step is to name a variable to represent the length of the first side. Let x be equal to the length of the first side, x plus 3 be equal to the length of the second side, and 2 x plus 2 be equal to the length of the third side. The figure is a triangle with sides labeled x, x plus 3, and 2 x plus 2, and a perimeter shown to be 29 inches. Step 4 is to translate. Write the appropriate formula, which is P is equal to a plus b plus c. Substitute in the given information. The result is 29 is equal to x plus the quantity x plus 3 plus the quantity 2 x plus 2. Step 5 is to solve the equation, 29 is equal to 4 x plus 5. 24 is equal to 4 x. 6 is equal to x, which is the length of the first side. The expression, x plus 3, is the length of the second side. The second side is 6 plus 3, which is equal to 9. The expression, 2 x plus 2, is the length of the second side. The second side is 2 times 6 plus 2, which is equal to 14. Step 6 is to check the answers. The figure is a triangle with sides labeled, 6, 9, and 14. Is 29 equal to 6 plus 9 plus 14? 29 is equal to 29, so the answers check. Step 7 is to answer the question. The lengths of the sides of the triangle are 6 inches, 9 inches, and 14 inches.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td data-valign=\"top\" data-align=\"left\">the lengths of the three sides of a triangle<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name<\/strong>. Choose a variable to<\/p>\n<div data-type=\"newline\"><\/div>\n<p>represent the length of the first side.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-58b7d9943c6a3a129b4f2f311bda5dde_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#76;&#101;&#116;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#108;&#101;&#110;&#103;&#116;&#104;&#32;&#111;&#102;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#116;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#105;&#100;&#101;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#120;&#43;&#51;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#108;&#101;&#110;&#103;&#116;&#104;&#32;&#111;&#102;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#50;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#105;&#100;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#120;&#43;&#50;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#108;&#101;&#110;&#103;&#116;&#104;&#32;&#111;&#102;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#51;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#105;&#100;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"226\" style=\"vertical-align: -25px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167831081604\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_014b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate.<\/strong><\/p>\n<div data-type=\"newline\"><\/div>\n<p>Write the appropriate formula.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Substitute in the given information.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167827987478\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_014c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167826849416\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_014d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167831883329\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_014e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check.<\/strong><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167835280400\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_014a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-57971760c5e8f444bfe7d0f6e931bc5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#57;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#54;&#43;&#57;&#43;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"121\" style=\"vertical-align: -2px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-873862b3937dd76e39407128b7000a9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#57;&#61;&#50;&#57;&#10003;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"60\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td>\n<td data-valign=\"top\" data-align=\"left\">The lengths of the sides of the triangle<\/p>\n<div data-type=\"newline\"><\/div>\n<p>are 6, 9, and 14 inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167830915027\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167830915030\">\n<div data-type=\"problem\" id=\"fs-id1167826874298\">\n<p id=\"fs-id1167826874300\">One side of a triangle is seven inches more than the first side. The third side is four inches less than three times the first. The perimeter is 28 inches. Find the length of the three sides of the triangle.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835304912\">\n<p id=\"fs-id1167831103756\">The lengths of the sides of the triangle are 5, 11 and 12 inches.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167834536419\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167834289509\">\n<div data-type=\"problem\" id=\"fs-id1167834289512\">\n<p id=\"fs-id1167834289514\">One side of a triangle is three feet less than the first side. The third side is five feet less than twice the first. The perimeter is 20 feet. Find the length of the three sides of the triangle.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167832116195\">\n<p id=\"fs-id1167832116197\">The lengths of the sides of the triangle are 4, 7 and 9 feet.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"example\" id=\"fs-id1167835395545\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167834422574\">\n<div data-type=\"problem\" id=\"fs-id1167834422576\">\n<p id=\"fs-id1167834422579\">The perimeter of a rectangular soccer field is 360 feet. The length is 40 feet more than the width. Find the length and width.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167835479858\" data-alt=\"The figure is an illustration of rectangular soccer field.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_015_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is an illustration of rectangular soccer field.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167835390424\">\n<table id=\"fs-id1167835524248\" class=\"unnumbered unstyled can-break\" summary=\"Step 1 is to read the problem. Step 2 is to identify what we are looking for. We are looking for the length and width of the soccer field. Step 3 is to name a variable to represent it. Let w be equal to the width. The length is 40 feet more than the width, so let w plus 40 be equal to the length. Draw the figure and label it with the given information. The figure is an illustration of a rectangular soccer field, its length labeled w and its width labeled w plus 40, and its perimeter given as 360 feet. Step 4 is to translate. Write the appropriate formula and substitute. The formula is P is equal to 2 L plus 2 W. 360 is equal to the sum of 2 times the quantity w plus 40 and 2 w. Step 5 is to solve the equation. 360 is equal to 2 w plus 80 plus 2 w. 360 is equal to 4 w plus 80. 280 is equal to 4 w. 70 is equal to w, which is the width of the field. The expression, w plus 40, is the length of the field. It is 70 plus 40, which is equal to 110. Step 6 is to check the answers. The perimeter is given by the formula, P is equal to 2 L plus 2 W. Is 360 equal to 2 times 110 plus 2 times 70? 360 is equal to 360, so the answers check. Step 7 is to answer the question. The length of the soccer field is 110 feet and the width is 70 feet.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td data-valign=\"top\" data-align=\"left\">the length and width of the soccer field<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name.<\/strong> Choose a variable to represent it.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>The length is 40 feet more than the width.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Draw the figure and label it with the<\/p>\n<div data-type=\"newline\"><\/div>\n<p>given information.<\/td>\n<td data-valign=\"top\" data-align=\"left\">Let <em data-effect=\"italics\">w<\/em> = width.<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7e6349920f67bcf4b18ac784886d9503_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;&#43;&#52;&#48;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"70\" style=\"vertical-align: -2px;\" \/> length<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167826870028\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_016a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate<\/strong>.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Write the appropriate formula and<\/p>\n<div data-type=\"newline\"><\/div>\n<p>substitute.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835595458\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_016b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167834423262\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_016c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835199569\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_016d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check.<\/strong><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cea901414cc8a38a05c792bc18d061f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#80;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#50;&#76;&#43;&#50;&#87;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#51;&#54;&#48;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#51;&#54;&#48;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#51;&#54;&#48;&#10003;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"189\" style=\"vertical-align: -25px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td>\n<td data-valign=\"top\" data-align=\"left\">The length of the soccer field is 110 feet<\/p>\n<div data-type=\"newline\"><\/div>\n<p>and the width is 70 feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167835358387\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167835358391\">\n<div data-type=\"problem\" id=\"fs-id1167835358393\">\n<p id=\"fs-id1167834184182\">The perimeter of a rectangular swimming pool is 200 feet. The length is 40 feet more than the width. Find the length and width.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834184188\">\n<p id=\"fs-id1167834184190\">The length of the swimming pool is 70 feet and the width is 30 feet.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167834535247\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167831894727\">\n<div data-type=\"problem\" id=\"fs-id1167831894729\">\n<p id=\"fs-id1167831894732\">The length of a rectangular garden is 30 yards more than the width. The perimeter is 300 yards. Find the length and width.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167826967250\">\n<p id=\"fs-id1167826967252\">The length of the garden is 90 yards and the width is 60 yards.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1166401363101\">Applications of these geometric properties can be found in many everyday situations as shown in the next example.<\/p>\n<div data-type=\"example\" id=\"fs-id1167834523812\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167834523814\">\n<div data-type=\"problem\" id=\"fs-id1167834523816\">\n<p id=\"fs-id1167835238919\">Kelvin is building a gazebo and wants to brace each corner by placing a 10\u201d piece of wood diagonally as shown.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167835238924\" data-alt=\"The figure is an illustration of a gazebo whose corner forms a right triangle with a 10 inch piece of wood that is placed diagonally to brace it.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_017_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is an illustration of a gazebo whose corner forms a right triangle with a 10 inch piece of wood that is placed diagonally to brace it.\" \/><\/span><\/p>\n<p id=\"fs-id1167835511283\">How far from the corner should he fasten the wood if wants the distances from the corner to be equal? Approximate to the nearest tenth of an inch.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835511288\">\n<table id=\"fs-id1167834079300\" class=\"unnumbered unstyled can-break\" summary=\"Step 1 is to read the problem. Step 2 is to identify what we are looking for. We are looking for the distance from the corner that the bracket should be attached. Step 3 is to name a variable to represent it. Let x be equal to the distance from the corner. Draw the figure and label it with the given information. The figure is right triangle with both sides labeled x and a hypotenuse labeled 10. Step 4 is to translate. Write the appropriate formula and substitute. The formula is a squared plus b squared is equal to c squared. By substituting, the result is x squared plus x squared is equal to 10 squared. Step 5 is to solve the equation, 2 x squared is equal to 100. Isolate the variable. The result is x squared is equal to 50. Use the definition of square root. x is equal to the square root of 50. Simplify. Approximate to the nearest tenth. The side, x, is approximately equal to 7.1. Step 6 is to check using the formula a squared plus b squared is equal to c squared. Is 7.1 squared plus 7.1 squared approximately equal to 10 squared. Yes. Step 7 is to answer the question. Kelvin should fasten each piece of wood approximately 7.1 inches from the corner.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what we are looking for.<\/td>\n<td data-valign=\"top\" data-align=\"left\">the distance from the corner that the<\/p>\n<div data-type=\"newline\"><\/div>\n<p>bracket should be attached<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name.<\/strong> Choose a variable to represent it.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Draw the figure and label it with the given<\/p>\n<div data-type=\"newline\"><\/div>\n<p>information.<\/td>\n<td data-valign=\"top\" data-align=\"left\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e7bbcde7229c9d7d6f7f2b6793961e97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"28\" style=\"vertical-align: 0px;\" \/> the distance from the corner.<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167834189737\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_018a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate.<\/strong><\/p>\n<div data-type=\"newline\"><\/div>\n<p>Write the appropriate formula and substitute.<\/td>\n<td data-valign=\"top\" data-align=\"left\">\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7ea02600b9972a334e42686c1b0b4cf4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#61;&#123;&#99;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"93\" style=\"vertical-align: -2px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0151046eda741ea30916bd62704c0bf3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#61;&#123;&#49;&#48;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"106\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Isolate the variable.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Use the definition of square root.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Simplify. Approximate to the nearest tenth.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6c105769696c6a224290e657be7fc169_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#125;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#49;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#53;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#120;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#48;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#120;&#38;&#32;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#55;&#46;&#49;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"259\" width=\"33\" style=\"vertical-align: -144px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check.<\/strong><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a4f961a26495da1548eb9ac74723b887_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#46;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#46;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#38;&#32;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#123;&#49;&#48;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#101;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"229\" style=\"vertical-align: -16px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td>\n<td data-valign=\"top\" data-align=\"left\">Kelvin should fasten each piece of wood<\/p>\n<div data-type=\"newline\"><\/div>\n<p>approximately 7.1\u201d from the corner.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167831921173\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167831921177\">\n<div data-type=\"problem\" id=\"fs-id1167827958374\">\n<p id=\"fs-id1167827958377\">John puts the base of a 13-foot ladder five feet from the wall of his house as shown in the figure. How far up the wall does the ladder reach?<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167827958381\" data-alt=\"The figure is an illustration that shows a ladder placed against the wall of a house. The ladder forms a right triangle with the side of the house. The ladder is 13 feet long and the base of the ladder is 5 feet from the wall of the house.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_019_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is an illustration that shows a ladder placed against the wall of a house. The ladder forms a right triangle with the side of the house. The ladder is 13 feet long and the base of the ladder is 5 feet from the wall of the house.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167835352143\">\n<p id=\"fs-id1167835352145\">The ladder reaches 12 feet.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167827987488\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167827987491\">\n<div data-type=\"problem\" id=\"fs-id1167827987493\">\n<p id=\"fs-id1167835287571\">Randy wants to attach a 17-foot string of lights to the top of the 15 foot mast of his sailboat, as shown in the figure. How far from the base of the mast should he attach the end of the light string?<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167835287576\" data-alt=\"The figure is an illustration of a sailboat that has a 15 foot mast. A string of lights that are 17 feet long are placed diagonally from the top of the mast.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_020_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is an illustration of a sailboat that has a 15 foot mast. A string of lights that are 17 feet long are placed diagonally from the top of the mast.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167835318900\">\n<p id=\"fs-id1167834539690\">He should attach the lights 8 feet from the base of the mast.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" class=\"media-2\">\n<p id=\"fs-id1167835513589\">Access this online resource for additional instruction and practice with solving for a variable in literal equations.<\/p>\n<ul id=\"fs-id1167835513593\" data-display=\"block\">\n<li><a href=\"https:\/\/openstax.org\/l\/37literalequat\">Solving Literal Equations<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167834495268\">\n<h3 data-type=\"title\">Key Concepts<\/h3>\n<ul id=\"fs-id1167835347888\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">How To Solve Geometry Applications<\/strong>\n<ol id=\"fs-id1167834190160\" type=\"1\" class=\"stepwise\">\n<li><strong data-effect=\"bold\">Read<\/strong> the problem and make sure all the words and ideas are understood.<\/li>\n<li><strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/li>\n<li><strong data-effect=\"bold\">Name<\/strong> what you are looking for by choosing a variable to represent it. Draw the figure and label it with the given information.<\/li>\n<li><strong data-effect=\"bold\">Translate<\/strong> into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.<\/li>\n<li><strong data-effect=\"bold\">Solve<\/strong> the equation using good algebra techniques.<\/li>\n<li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem and make sure it makes sense.<\/li>\n<li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">The Pythagorean Theorem<\/strong>\n<ul id=\"fs-id1167831191490\" data-bullet-style=\"open-circle\">\n<li>In any right triangle, where <em data-effect=\"italics\">a<\/em> and <em data-effect=\"italics\">b<\/em> are the lengths of the legs, and <em data-effect=\"italics\">c<\/em> is the length of the hypotenuse, the sum of the squares of the lengths of the two legs equals the square of the length of the hypotenuse.\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1167835231077\" data-alt=\"The figure is a right triangle with sides a and b, and a hypotenuse c with the formula, a squared plus b squared is equal to c squared.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_021_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides a and b, and a hypotenuse c with the formula, a squared plus b squared is equal to c squared.\" \/><\/span> <\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167835356559\">\n<div class=\"practice-perfect\" data-depth=\"2\" id=\"fs-id1167826895638\">\n<h4 data-type=\"title\">Practice Makes Perfect<\/h4>\n<p id=\"fs-id1167826895645\"><strong data-effect=\"bold\">Solve a Formula for a Specific Variable<\/strong><\/p>\n<p id=\"fs-id1167835342505\">In the following exercises, solve the given formula for the specified variable.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167835342508\">\n<div data-type=\"problem\" id=\"fs-id1167835342510\">\n<p id=\"fs-id1167832144313\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d53af99f4271505ce26601a2fb3edbbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#92;&#112;&#105;&#32;&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"58\" style=\"vertical-align: 0px;\" \/> for <em data-effect=\"italics\">d<\/em>.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167831892225\">\n<p id=\"fs-id1167831892227\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3d18a6421b9c6833861ca250a58924a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#67;&#125;&#123;&#92;&#112;&#105;&#32;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"46\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832054581\">\n<div data-type=\"problem\" id=\"fs-id1167832054583\">\n<p id=\"fs-id1167832099503\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d53af99f4271505ce26601a2fb3edbbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#92;&#112;&#105;&#32;&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"58\" style=\"vertical-align: 0px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-445d7c74b1b048e6d603e79a72281a3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;&#32;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834479640\">\n<div data-type=\"problem\" id=\"fs-id1167834526234\">\n<p id=\"fs-id1167834526236\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-70441d53f3f0f6969e5be735ccb8b3f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#76;&#87;&#72;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"85\" style=\"vertical-align: 0px;\" \/> for <em data-effect=\"italics\">L<\/em>.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835304084\">\n<p id=\"fs-id1167835304086\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-17b4a237a5621549700f9bd7d5ce60f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#76;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#86;&#125;&#123;&#87;&#72;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835420838\">\n<div data-type=\"problem\" id=\"fs-id1167835420840\">\n<p id=\"fs-id1167835420842\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-70441d53f3f0f6969e5be735ccb8b3f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#76;&#87;&#72;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"85\" style=\"vertical-align: 0px;\" \/> for <em data-effect=\"italics\">H<\/em>.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826781501\">\n<div data-type=\"problem\" id=\"fs-id1167826781504\">\n<p id=\"fs-id1167826781506\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b372c8f17c232fb83c5e06a24bf6fd73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/> for <em data-effect=\"italics\">b<\/em>.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835420974\">\n<p id=\"fs-id1167835420976\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a0d9397e145e622bd2b77dc4fdb9d7a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#65;&#125;&#123;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"51\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834309031\">\n<div data-type=\"problem\" id=\"fs-id1167834309033\">\n<p id=\"fs-id1167834309035\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b372c8f17c232fb83c5e06a24bf6fd73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/> for <em data-effect=\"italics\">h<\/em>.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167831911306\">\n<div data-type=\"problem\" id=\"fs-id1167831911308\">\n<p id=\"fs-id1167834190492\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5fdad0cf7dcfb87f40734deb99647d1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#123;&#100;&#125;&#95;&#123;&#49;&#125;&#123;&#100;&#125;&#95;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"81\" style=\"vertical-align: -6px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-24cbe3383189e5537c29f6799d8d63b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#100;&#125;&#95;&#123;&#49;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"21\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167826978562\">\n<p id=\"fs-id1167826978565\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-23936fdaa9acec9ad242d2dfbbcfa70a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#100;&#125;&#95;&#123;&#49;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#65;&#125;&#123;&#123;&#100;&#125;&#95;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"60\" style=\"vertical-align: -8px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167828240458\">\n<div data-type=\"problem\" id=\"fs-id1167828240460\">\n<p id=\"fs-id1167834299558\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5fdad0cf7dcfb87f40734deb99647d1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#123;&#100;&#125;&#95;&#123;&#49;&#125;&#123;&#100;&#125;&#95;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"81\" style=\"vertical-align: -6px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-93e860f227b56edaf8e3e95498cee86e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#100;&#125;&#95;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -3px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832057420\">\n<div data-type=\"problem\" id=\"fs-id1167832057422\">\n<p id=\"fs-id1167832057424\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4c5578ce8a377dc7b0d73dbfe21f5671_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#98;&#125;&#95;&#123;&#49;&#125;&#43;&#123;&#98;&#125;&#95;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"126\" style=\"vertical-align: -6px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cba6da62213a29259e74a81377057cfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#95;&#123;&#49;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"19\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167834214014\">\n<p id=\"fs-id1167834214016\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fc2a74bc083479c1e311cc37399444ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#95;&#123;&#49;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#65;&#125;&#123;&#104;&#125;&#45;&#123;&#98;&#125;&#95;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"97\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167831872472\">\n<div data-type=\"problem\" id=\"fs-id1167831872475\">\n<p id=\"fs-id1167831872477\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4c5578ce8a377dc7b0d73dbfe21f5671_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#98;&#125;&#95;&#123;&#49;&#125;&#43;&#123;&#98;&#125;&#95;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"126\" style=\"vertical-align: -6px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-76c38e875c5bb3ac2716e08819ded2fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#95;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"19\" style=\"vertical-align: -3px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835331684\">\n<div data-type=\"problem\" id=\"fs-id1167835331686\">\n<p id=\"fs-id1167826998344\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-24bb058977372214bfbdba21ff3cf0e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#61;&#53;&#52;&#116;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#97;&#123;&#116;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"112\" style=\"vertical-align: -6px;\" \/> for <em data-effect=\"italics\">a<\/em>.<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834193737\">\n<p id=\"fs-id1167835333648\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b79c593ca0fefd3fb5b301c18f838b04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#104;&#45;&#49;&#48;&#56;&#116;&#125;&#123;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"87\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834319817\">\n<div data-type=\"problem\" id=\"fs-id1167834319819\">\n<p id=\"fs-id1167834319822\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-944460697cc806861b0c6e0213feedd8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#61;&#52;&#56;&#116;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#97;&#123;&#116;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"112\" style=\"vertical-align: -6px;\" \/> for <em data-effect=\"italics\">a<\/em>.<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835415629\">\n<div data-type=\"problem\" id=\"fs-id1167831892284\">\n<p id=\"fs-id1167831892286\">Solve <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-624842cf5acdd7754579a3eca415ebb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#48;&#61;&#97;&#43;&#98;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"118\" style=\"vertical-align: -2px;\" \/> for <em data-effect=\"italics\">a<\/em>.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834439048\">\n<p id=\"fs-id1167834439050\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90f85debce819418e6b525cbda1e0ef6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#49;&#56;&#48;&#45;&#98;&#45;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"119\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834592990\">\n<div data-type=\"problem\" id=\"fs-id1167834592992\">\n<p id=\"fs-id1167835417763\">Solve <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-624842cf5acdd7754579a3eca415ebb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#48;&#61;&#97;&#43;&#98;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"118\" style=\"vertical-align: -2px;\" \/> for <em data-effect=\"italics\">c<\/em>.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167831824332\">\n<div data-type=\"problem\" id=\"fs-id1167831824335\">\n<p id=\"fs-id1167831824337\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-572f0f53fe460e405babaf6074a86865_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#112;&#108;&#43;&#66;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"98\" style=\"vertical-align: -6px;\" \/> for <em data-effect=\"italics\">p<\/em>.<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834505436\">\n<p id=\"fs-id1167834505438\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c23d5065c8ae3f709e20ab2f28a35a6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#65;&#45;&#50;&#66;&#125;&#123;&#108;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"81\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835189598\">\n<div data-type=\"problem\" id=\"fs-id1167835189601\">\n<p id=\"fs-id1167835189603\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-572f0f53fe460e405babaf6074a86865_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#112;&#108;&#43;&#66;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"98\" style=\"vertical-align: -6px;\" \/> for <em data-effect=\"italics\">l<\/em>.<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835380611\">\n<div data-type=\"problem\" id=\"fs-id1167831894377\">\n<p id=\"fs-id1167831894379\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fd41d005b7610a456dc9e5dc6ad9fd67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#50;&#76;&#43;&#50;&#87;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"108\" style=\"vertical-align: -2px;\" \/> for <em data-effect=\"italics\">L<\/em>.<\/div>\n<div data-type=\"solution\" id=\"fs-id1167831112470\">\n<p id=\"fs-id1167831112472\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ce2ccbf85c39e38c0981dbb6d21c9aeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#76;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#80;&#45;&#50;&#87;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"82\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835420752\">\n<div data-type=\"problem\" id=\"fs-id1167835420754\">\n<p id=\"fs-id1167835498611\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fd41d005b7610a456dc9e5dc6ad9fd67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#50;&#76;&#43;&#50;&#87;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"108\" style=\"vertical-align: -2px;\" \/> for <em data-effect=\"italics\">W<\/em>.<\/div>\n<\/div>\n<p id=\"fs-id1167835515258\">In the following exercises, solve for the formula for <em data-effect=\"italics\">y<\/em>.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167831824988\">\n<div data-type=\"problem\" id=\"fs-id1167831824990\">\n<p id=\"fs-id1167831824992\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-874101efc8be87c595db3aeaab7e8799_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#43;&#121;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"91\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y<\/em>.<\/div>\n<div data-type=\"solution\" id=\"fs-id1167830703747\">\n<p id=\"fs-id1167830703749\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8020d1db21494e1bd9eb972393a4a01b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#49;&#53;&#45;&#56;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835319368\">\n<div data-type=\"problem\" id=\"fs-id1167835319370\">\n<p id=\"fs-id1167835319372\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0fa0ca94516e06fa9e3aba945ce33f0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#120;&#43;&#121;&#61;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"92\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y<\/em>.<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832058756\">\n<div data-type=\"problem\" id=\"fs-id1167832058758\">\n<p id=\"fs-id1167832058760\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-249f8726b532ecb033c1a59d2a46d4cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#120;&#43;&#121;&#61;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"109\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y<\/em>.<\/div>\n<div data-type=\"solution\" id=\"fs-id1167831880819\">\n<p id=\"fs-id1167831880821\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2414d64e8155b56f5b5f9e5ec0cf7383_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#54;&#43;&#52;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834300891\">\n<div data-type=\"problem\" id=\"fs-id1167834300893\">\n<p id=\"fs-id1167834300895\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8ed60d38f3302f1caa25ffa7d3e1030a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#120;&#43;&#121;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"108\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y<\/em>.<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835518375\">\n<div data-type=\"problem\" id=\"fs-id1167826819375\">\n<p id=\"fs-id1167826819377\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4130f8c9dac07d3b719f961e72ec907e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#121;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"88\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y<\/em>.<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834324635\">\n<p id=\"fs-id1167834324637\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8ca89ab7604a9d148cbef614f7b43648_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;&#43;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835236061\">\n<div data-type=\"problem\" id=\"fs-id1167835236063\">\n<p id=\"fs-id1167835236065\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-563815f4b4ab31329141b981dfcb68e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#121;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"88\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y<\/em>.<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834192344\">\n<div data-type=\"problem\" id=\"fs-id1167834192346\">\n<p id=\"fs-id1167834192349\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-21ade233c63be6c181124b1c2c20bb5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#51;&#121;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"91\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y<\/em>.<\/div>\n<div data-type=\"solution\" id=\"fs-id1167831880016\">\n<p id=\"fs-id1167831880018\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f21aa0d915943afc6c26eb3e06641a2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#45;&#52;&#120;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834506155\">\n<div data-type=\"problem\" id=\"fs-id1167834506157\">\n<p id=\"fs-id1167834506160\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3eae86ee092a5ecc6a15d06c51715eb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"99\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y<\/em>.<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832087113\">\n<div data-type=\"problem\" id=\"fs-id1167830865704\">\n<p id=\"fs-id1167830865706\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-81bf3fe4432aa807b30107962af3db18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#51;&#121;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"99\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y<\/em>.<\/div>\n<div data-type=\"solution\" id=\"fs-id1167828421269\">\n<p id=\"fs-id1167828421272\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-257e63125fe06f01035194a85d6d0a7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#45;&#50;&#120;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835420241\">\n<div data-type=\"problem\" id=\"fs-id1167835420243\">\n<p id=\"fs-id1167835327442\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-79b727dd3be137db9ceda850e7b18c09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#43;&#50;&#121;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y<\/em>.<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832065987\">\n<div data-type=\"problem\" id=\"fs-id1167832065989\">\n<p id=\"fs-id1167832065992\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-dbf6962d9940ce295c31d36a08504c09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#50;&#121;&#61;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"100\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y<\/em>.<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834428843\">\n<p id=\"fs-id1167834428846\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-11f903402fc9f61a0a538c986466fd05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#56;&#45;&#51;&#120;&#125;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835319959\">\n<div data-type=\"problem\" id=\"fs-id1167835319962\">\n<p id=\"fs-id1167835319964\">Solve the formula<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-efedfb1adc9ce250cfc862e4fb07e730_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#45;&#51;&#121;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"99\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y<\/em>.<\/div>\n<\/div>\n<p id=\"fs-id1167834130084\"><strong data-effect=\"bold\">Use Formulas to Solve Geometry Applications<\/strong><\/p>\n<p id=\"fs-id1167834130091\">In the following exercises, solve using a geometry formula.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167831894321\">\n<div data-type=\"problem\" id=\"fs-id1167831894323\">\n<p id=\"fs-id1167831894326\">A triangular flag has area 0.75 square feet and height 1.5 foot. What is its base?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167831894330\">\n<p id=\"fs-id1167831894332\">1 foot<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167830757264\">\n<div data-type=\"problem\" id=\"fs-id1167830757267\">\n<p id=\"fs-id1167830757269\">A triangular window has area 24 square feet and height six feet. What is its base?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826779531\">\n<div data-type=\"problem\" id=\"fs-id1167826779533\">\n<p id=\"fs-id1167826779536\">What is the base of a triangle with area 207 square inches and height 18 inches?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167826779540\">\n<p id=\"fs-id1167826779542\">23 inches<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167831888080\">\n<div data-type=\"problem\" id=\"fs-id1167831888082\">\n<p id=\"fs-id1167831888084\">What is the height of a triangle with area 893 square inches and base 38 inches?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835483782\">\n<div data-type=\"problem\" id=\"fs-id1167835483784\">\n<p id=\"fs-id1167835483786\">The two smaller angles of a right triangle have equal measures. Find the measures of all three angles.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835370677\">\n<p id=\"fs-id1167835370679\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-269a9b6fdadff012f66fee71530c5dd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#53;&#92;&#116;&#101;&#120;&#116;&#123;&deg;&#125;&#44;&#52;&#53;&#92;&#116;&#101;&#120;&#116;&#123;&deg;&#125;&#44;&#57;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&deg;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"69\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834526616\">\n<div data-type=\"problem\" id=\"fs-id1167834526618\">\n<p id=\"fs-id1167826983749\">The measure of the smallest angle of a right triangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-74f80a542e12b1cd2f0b27d4a2fe535c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&deg;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> less than the measure of the next larger angle. Find the measures of all three angles.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167831921553\">\n<div data-type=\"problem\" id=\"fs-id1167831921555\">\n<p id=\"fs-id1167831921557\">The angles in a triangle are such that one angle is twice the smallest angle, while the third angle is three times as large as the smallest angle. Find the measures of all three angles.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835420912\">\n<p id=\"fs-id1167835420914\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-15e239cf1e06573729fe06fd1829f65d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&deg;&#125;&#44;&#54;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&deg;&#125;&#44;&#57;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&deg;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"69\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834535231\">\n<div data-type=\"problem\" id=\"fs-id1167832042513\">\n<p id=\"fs-id1167832042515\">The angles in a triangle are such that one angle is 20 more than the smallest angle, while the third angle is three times as large as the smallest angle. Find the measures of all three angles.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167834556835\">In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167834556838\">\n<div data-type=\"problem\" id=\"fs-id1167834556840\"><span data-type=\"media\" id=\"fs-id1167834556841\" data-alt=\"The figure is a right triangle with sides 9 units and 12 units.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_201_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides 9 units and 12 units.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167835359874\">\n<p id=\"fs-id1167835359876\">15<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834367209\">\n<div data-type=\"problem\" id=\"fs-id1167834367211\"><span data-type=\"media\" id=\"fs-id1167834367212\" data-alt=\"The figure is a right triangle with sides 16 units and 12 units.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_202_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides 16 units and 12 units.\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834280016\">\n<div data-type=\"problem\" id=\"fs-id1167834280019\"><span data-type=\"media\" id=\"fs-id1167834280020\" data-alt=\"The figure is a right triangle with sides 15 units and 20 units.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_203_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides 15 units and 20 units.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167834179724\">\n<p id=\"fs-id1167834179726\">25<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835307426\">\n<div data-type=\"problem\" id=\"fs-id1167835307428\"><span data-type=\"media\" id=\"fs-id1167835307429\" data-alt=\"The figure is a right triangle with sides 5 units and 12 units.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_204_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides 5 units and 12 units.\" \/><\/span><\/div>\n<\/div>\n<p id=\"fs-id1167828420159\">In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth if necessary.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167835274878\">\n<div data-type=\"problem\" id=\"fs-id1167835274880\"><span data-type=\"media\" id=\"fs-id1167835274881\" data-alt=\"The figure is a right triangle with sides 6 units and 10 units.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_205_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides 6 units and 10 units.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167831836516\">\n<p id=\"fs-id1167831836518\">8<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167831836523\">\n<div data-type=\"problem\" id=\"fs-id1167831836526\"><span data-type=\"media\" id=\"fs-id1167831836527\" data-alt=\"The figure is a right triangle with a side that is 9 units and a hypotenuse that is 13 units.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_206_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with a side that is 9 units and a hypotenuse that is 13 units.\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835319680\">\n<div data-type=\"problem\" id=\"fs-id1167835319682\"><span data-type=\"media\" id=\"fs-id1167835319683\" data-alt=\"The figure is a right triangle with a side that is 5 units and a hypotenuse that is 13 units.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_207_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with a side that is 5 units and a hypotenuse that is 13 units.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167830694080\">\n<p id=\"fs-id1167830694082\">12<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167830694087\">\n<div data-type=\"problem\" id=\"fs-id1167830694090\"><span data-type=\"media\" id=\"fs-id1167830694091\" data-alt=\"The figure is a right triangle with a side that is 16 units and a hypotenuse that is 20 units.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_208_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with a side that is 16 units and a hypotenuse that is 20 units.\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832031167\">\n<div data-type=\"problem\" id=\"fs-id1167832031169\"><span data-type=\"media\" id=\"fs-id1167832031170\" data-alt=\"The figure is a right triangle with a side that is 8 units and a hypotenuse that is 13 units.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_209_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with a side that is 8 units and a hypotenuse that is 13 units.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167835511301\">\n<p id=\"fs-id1167835511303\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-032962f9dd5b2a36269d9fe3aaa4c573_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834505182\">\n<div data-type=\"problem\" id=\"fs-id1167834505184\"><span data-type=\"media\" id=\"fs-id1167834505186\" data-alt=\"The figure is a right triangle with sides that are both 6 units.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_210_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides that are both 6 units.\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834192417\">\n<div data-type=\"problem\" id=\"fs-id1167831825080\"><span data-type=\"media\" id=\"fs-id1167831825081\" data-alt=\"The figure is a right triangle with sides that are 5 units and 11 units.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_211_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides that are 5 units and 11 units.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167831825093\">\n<p id=\"fs-id1167835357419\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d3d09cac85974f054211080cd7fcbe20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#46;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835357427\">\n<div data-type=\"problem\" id=\"fs-id1167835357430\"><span data-type=\"media\" id=\"fs-id1167835357431\" data-alt=\"The figure is a right triangle with sides that are 5 units and 7 units.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_212_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is a right triangle with sides that are 5 units and 7 units.\" \/><\/span><\/div>\n<\/div>\n<p id=\"fs-id1167835351900\">In the following exercises, solve using a geometry formula.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167835351903\">\n<div data-type=\"problem\" id=\"fs-id1167835351905\">\n<p id=\"fs-id1167835351908\">The width of a rectangle is seven meters less than the length. The perimeter is 58 meters. Find the length and width.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835369827\">\n<p id=\"fs-id1167835369829\">18 meters, 11 meters<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835369834\">\n<div data-type=\"problem\" id=\"fs-id1167835369836\">\n<p id=\"fs-id1167831933905\">The length of a rectangle is eight feet more than the width. The perimeter is 60 feet. Find the length and width.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167831933918\">\n<div data-type=\"problem\" id=\"fs-id1167826857090\">\n<p id=\"fs-id1167826857092\">The width of the rectangle is 0.7 meters less than the length. The perimeter of a rectangle is 52.6 meters. Find the dimensions of the rectangle.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167832075583\">\n<p id=\"fs-id1167832075585\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-69fd8e167c9226d1659f5d42e99658c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"30\" style=\"vertical-align: -1px;\" \/> m, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-de3557022593204f992aff4e87ba6e8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#46;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> m<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834131256\">\n<div data-type=\"problem\" id=\"fs-id1167834131258\">\n<p id=\"fs-id1167834131260\">The length of the rectangle is 1.1 meters less than the width. The perimeter of a rectangle is 49.4 meters. Find the dimensions of the rectangle.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826978925\">\n<div data-type=\"problem\" id=\"fs-id1167826978927\">\n<p id=\"fs-id1167835623450\">The perimeter of a rectangle of 150 feet. The length of the rectangle is twice the width. Find the length and width of the rectangle.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835623455\">\n<p id=\"fs-id1167835623458\">25 ft, 50 ft<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835623463\">\n<div data-type=\"problem\" id=\"fs-id1167826874392\">\n<p id=\"fs-id1167826874395\">The length of the rectangle is three times the width. The perimeter of a rectangle is 72 feet. Find the length and width of the rectangle.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835238812\">\n<div data-type=\"problem\" id=\"fs-id1167835238814\">\n<p id=\"fs-id1167835238816\">The length of the rectangle is three meters less than twice the width. The perimeter of a rectangle is 36 meters. Find the dimensions of the rectangle.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835238822\">\n<p id=\"fs-id1167835238824\">7 m, 11 m<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834534825\">\n<div data-type=\"problem\">\n<p id=\"fs-id1167834534830\">The length of a rectangle is five inches more than twice the width. The perimeter is 34 inches. Find the length and width.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834098370\">\n<div data-type=\"problem\" id=\"fs-id1167834098372\">\n<p id=\"fs-id1167834098375\">The perimeter of a triangle is 39 feet. One side of the triangle is one foot longer than the second side. The third side is two feet longer than the second side. Find the length of each side.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834152069\">\n<p id=\"fs-id1167834152071\">12 ft, 13 ft, 14 ft<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834152076\">\n<div data-type=\"problem\" id=\"fs-id1167834152078\">\n<p id=\"fs-id1167834152080\">The perimeter of a triangle is 35 feet. One side of the triangle is five feet longer than the second side. The third side is three feet longer than the second side. Find the length of each side.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834280036\">\n<div data-type=\"problem\" id=\"fs-id1167834280039\">\n<p id=\"fs-id1167826941193\">One side of a triangle is twice the smallest side. The third side is five feet more than the shortest side. The perimeter is 17 feet. Find the lengths of all three sides.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167826941199\">\n<p id=\"fs-id1167826941201\">3 ft, 6 ft, 8 ft<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826941207\">\n<div data-type=\"problem\" id=\"fs-id1167834372298\">\n<p id=\"fs-id1167834372300\">One side of a triangle is three times the smallest side. The third side is three feet more than the shortest side. The perimeter is 13 feet. Find the lengths of all three sides.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167831892734\">\n<div data-type=\"problem\" id=\"fs-id1167831892736\">\n<p id=\"fs-id1167831892739\">The perimeter of a rectangular field is 560 yards. The length is 40 yards more than the width. Find the length and width of the field.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167831892744\">\n<p id=\"fs-id1167831892746\">120 yd, 160 yd<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826994856\">\n<div data-type=\"problem\" id=\"fs-id1167826994858\">\n<p id=\"fs-id1167826994860\">The perimeter of a rectangular atrium is 160 feet. The length is 16 feet more than the width. Find the length and width of the atrium.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167831921653\">\n<div data-type=\"problem\" id=\"fs-id1167831921655\">\n<p id=\"fs-id1167831921657\">A rectangular parking lot has perimeter 250 feet. The length is five feet more than twice the width. Find the length and width of the parking lot.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167831921663\">\n<p id=\"fs-id1167834314777\">40 ft, 85 ft<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834314783\">\n<div data-type=\"problem\" id=\"fs-id1167834314785\">\n<p id=\"fs-id1167834314787\">A rectangular rug has perimeter 240 inches. The length is 12 inches more than twice the width. Find the length and width of the rug.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167835301802\">In the following exercises, solve. Approximate answers to the nearest tenth, if necessary.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167835301805\">\n<div data-type=\"problem\" id=\"fs-id1167835301807\">\n<p id=\"fs-id1167835369467\">A 13-foot string of lights will be attached to the top of a 12-foot pole for a holiday display as shown. How far from the base of the pole should the end of the string of lights be anchored?<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167835369472\" data-alt=\"The figure is an illustration that shows a 13 foot string of lights attached diagonally to the top of a 12 foot pole.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_213_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is an illustration that shows a 13 foot string of lights attached diagonally to the top of a 12 foot pole.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167834526266\">\n<p id=\"fs-id1167834526268\">5 feet<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834526273\">\n<div data-type=\"problem\" id=\"fs-id1167834526276\">\n<p id=\"fs-id1167831883120\">am wants to put a banner across her garage door diagonally, as shown, to congratulate her son for his college graduation. The garage door is 12 feet high and 16 feet wide. Approximately how long should the banner be to fit the garage door?<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167831883125\" data-alt=\"The figure is an illustration of a banner positioned diagonally across a garage door that is 12 feet high and 16 feet wide.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_214_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is an illustration of a banner positioned diagonally across a garage door that is 12 feet high and 16 feet wide.\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835374354\">\n<div data-type=\"problem\" id=\"fs-id1167835374356\">\n<p id=\"fs-id1167831923518\">Chi is planning to put a diagonal path of paving stones through her flower garden as shown. The flower garden is a square with side 10 feet. What will the length of the path be?<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167831923522\" data-alt=\"The figure is an illustration of a diagonal path of stones through a square garden with 10 foot sides.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_215_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is an illustration of a diagonal path of stones through a square garden with 10 foot sides.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167835328668\">\n<p id=\"fs-id1167835328670\">14.1 feet<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835328676\">\n<div data-type=\"problem\" id=\"fs-id1167835328678\">\n<p id=\"fs-id1167832052679\">Brian borrowed a 20-foot extension ladder to use when he paints his house. If he sets the base of the ladder six feet from the house as shown, how far up will the top of the ladder reach?<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167832052684\" data-alt=\"The figure is an illustration of a house that has a ladder against it. The ladder is 20 feet. Its base is positioned 6 feet from the house.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_216_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure is an illustration of a house that has a ladder against it. The ladder is 20 feet. Its base is positioned 6 feet from the house.\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div class=\"everyday\" data-depth=\"2\" id=\"fs-id1167835595163\">\n<h4 data-type=\"title\">Everyday Math<\/h4>\n<div data-type=\"exercise\" id=\"fs-id1167835513249\">\n<div data-type=\"problem\" id=\"fs-id1167835513251\">\n<p id=\"fs-id1167835513253\"><strong data-effect=\"bold\">Converting temperature<\/strong> While on a tour in Greece, Tatyana saw that the temperature was 40\u00b0 Celsius. Solve for <em data-effect=\"italics\">F<\/em> in the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-827f8035affe1c5d4cfd48235dc2918d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#57;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#70;&#45;&#51;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"118\" style=\"vertical-align: -6px;\" \/> to find the Fahrenheit temperature.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167827940346\">\n<p id=\"fs-id1167827940349\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d580478eb69134041b55eb96e8d98592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#52;&#92;&#116;&#101;&#120;&#116;&#123;&deg;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835640088\">\n<div data-type=\"problem\" id=\"fs-id1167835640090\">\n<p id=\"fs-id1167835640092\"><strong data-effect=\"bold\">Converting temperature<\/strong> Yon was visiting the United States and he saw that the temperature in Seattle one day was 50\u00b0 Fahrenheit. Solve for <em data-effect=\"italics\">C<\/em> in the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0eae5cacfec517ea5c3fe4b03a538cd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#53;&#125;&#67;&#43;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"101\" style=\"vertical-align: -6px;\" \/> to find the Celsius temperature.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834396122\">\n<div data-type=\"problem\" id=\"fs-id1167834396124\">\n<p id=\"fs-id1167834396126\">Christa wants to put a fence around her triangular flowerbed. The sides of the flowerbed are six feet, eight feet and 10 feet. How many feet of fencing will she need to enclose her flowerbed?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834396132\">\n<p id=\"fs-id1167834396134\">24 ft<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834536483\">\n<div data-type=\"problem\" id=\"fs-id1167834536485\">\n<p id=\"fs-id1167834536487\">Jose just removed the children\u2019s play set from his back yard to make room for a rectangular garden. He wants to put a fence around the garden to keep the dog out. He has a 50-foot roll of fence in his garage that he plans to use. To fit in the backyard, the width of the garden must be 10 feet. How long can he make the other side?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"writing\" data-depth=\"2\" id=\"fs-id1167834536491\">\n<h4 data-type=\"title\">Writing Exercises<\/h4>\n<div data-type=\"exercise\" id=\"fs-id1167834527706\">\n<div data-type=\"problem\" id=\"fs-id1167834527708\">\n<p id=\"fs-id1167834527710\">If you need to put tile on your kitchen floor, do you need to know the perimeter or the area of the kitchen? Explain your reasoning.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834527715\">\n<p id=\"fs-id1167830960523\">Answers will vary.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167830960528\">\n<div data-type=\"problem\" id=\"fs-id1167830960530\">\n<p id=\"fs-id1167830960532\">If you need to put a fence around your backyard, do you need to know the perimeter or the area of the backyard? Explain your reasoning.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835410188\">\n<div data-type=\"problem\" id=\"fs-id1167835410190\">\n<p id=\"fs-id1167835410192\">Look at the two figures below.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167834464375\" data-alt=\"A figure of a rectangle with a width that is 2 units and a length that is 8 units and a square with sides that are 4 units.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_217_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"A figure of a rectangle with a width that is 2 units and a length that is 8 units and a square with sides that are 4 units.\" \/><\/span><\/p>\n<p id=\"fs-id1167834464388\"><span class=\"token\">\u24d0<\/span> Which figure looks like it has the larger area? Which looks like it has the larger perimeter?<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> Now calculate the area and perimeter of each figure. Which has the larger area? Which has the larger perimeter?<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span> Were the results of part (b) the same as your answers in part (a)? Is that surprising to you?<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835498857\">\n<p id=\"fs-id1167835498859\"><span class=\"token\">\u24d0<\/span> Answers will vary. <span class=\"token\">\u24d1<\/span> The areas are the same. The <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2c73b54d1bcab0c39534a8f25a2139f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&times;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"25\" style=\"vertical-align: 0px;\" \/> rectangle has a larger perimeter than the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c144d43134c9472013d40b973a2aada2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&times;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"25\" style=\"vertical-align: -1px;\" \/> square.<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span> Answers will vary.<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835488632\">\n<div data-type=\"problem\" id=\"fs-id1167835488634\">\n<p id=\"fs-id1167835488636\">Write a geometry word problem that relates to your life experience, then solve it and explain all your steps.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167831920420\">\n<h4 data-type=\"title\">Self Check<\/h4>\n<p id=\"fs-id1167831920426\"><span class=\"token\">\u24d0<\/span> After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167834517528\" data-alt=\"This table has four columns and three rows. The first row is a header and it labels each column, \u201cI can\u2026\u201d, \u201cConfidently,\u201d \u201cWith some help,\u201d and \u201cNo-I don\u2019t get it!\u201d In row 2, the I can was solve a formula for a specific variable. In row 3, the I can was use formulas to solve geometry applications.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_03_218_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This table has four columns and three rows. The first row is a header and it labels each column, \u201cI can\u2026\u201d, \u201cConfidently,\u201d \u201cWith some help,\u201d and \u201cNo-I don\u2019t get it!\u201d In row 2, the I can was solve a formula for a specific variable. In row 3, the I can was use formulas to solve geometry applications.\" \/><\/span><\/p>\n<p id=\"fs-id1167835375366\"><span class=\"token\">\u24d1<\/span> What does this checklist tell you about your mastery of this section? What steps will you take to improve?<\/p>\n<\/div>\n<\/div>\n","protected":false},"author":103,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1269","chapter","type-chapter","status-publish","hentry"],"part":991,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/1269","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/users\/103"}],"version-history":[{"count":1,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/1269\/revisions"}],"predecessor-version":[{"id":15152,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/1269\/revisions\/15152"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/parts\/991"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/1269\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/media?parent=1269"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapter-type?post=1269"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/contributor?post=1269"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/license?post=1269"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}