{"id":1401,"date":"2019-06-20T16:35:30","date_gmt":"2019-06-20T20:35:30","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1401"},"modified":"2019-10-29T12:24:41","modified_gmt":"2019-10-29T16:24:41","slug":"answer-key-4-5","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-4-5\/","title":{"raw":"Answer Key 4.5","rendered":"Answer Key 4.5"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(L=2W-3 \\text{ and } P=2L+2W \\Rightarrow 54=2(2W-3)+2W\\)<\/li>\r\n \t
  2. \\(L=2W-8 \\text{ and } P=2L+2W \\Rightarrow 64=2(2W-8)+2W\\)<\/li>\r\n \t
  3. \\(L=2W+4 \\text{ and } P=2L+2W \\Rightarrow 32=2(2W+4)+2W\\)<\/li>\r\n \t
  4. \\(A_1=2A_2, A_1=10^{\\circ}+A_3, A_1+A_2+A_3=180^{\\circ} \\Rightarrow\\)\r\n\\(A_1+\\dfrac{A_1}{2}+A_1- 10^{\\circ}=180^{\\circ}\\)<\/li>\r\n \t
  5. \\(A_1=\\dfrac{1}{2}A_2, A_1=20^{\\circ}+A_3, A_1+A_2+A_3=180^{\\circ} \\Rightarrow\\)\r\n\\(A_1+2A_1+A_1-20^{\\circ}=180^{\\circ}\\)<\/li>\r\n \t
  6. \\(A_1+A_2=\\dfrac{1}{2}A_3, A_1+A_2+A_3=180^{\\circ} \\Rightarrow\\)\r\n\\(\\dfrac{3}{2}A_3=180^{\\circ}\\hspace{0.34in} A_1 \\text{ and } A_2?\\)<\/li>\r\n \t
  7. \\(x_1+x_2=140, x_1=5x_2 \\Rightarrow 5x_2+x_2=140\\)<\/li>\r\n \t
  8. \\(x_1+x_2=48, x_2=5+x_1 \\Rightarrow x_1+5+x_1=48\\)<\/li>\r\n \t
  9. \\(\\begin{array}{rrrrrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nA_2&=&A_1&&&&&&&&&& \\\\\r\nA_3&=&A_1&+&12&&&&&&&& \\\\ \\\\\r\nA_1&+&A_2&+&A_3&&&=&180&&&& \\\\\r\nA_1&+&A_1&+&A_1&+&12&=&180&&&& \\\\\r\n&&&&&-&12&&-12&&&& \\\\\r\n\\midrule\r\n&&&&&&3A_1&=&168&&&& \\\\ \\\\\r\n&&&&&&A_1&=&\\dfrac{168}{3}&=&56&& \\\\\r\nA_1&=&56^{\\circ}&&&&&&&&&& \\\\\r\nA_2&=&56^{\\circ}&&&&&&&&&& \\\\\r\nA_3&=&56^{\\circ}&+&12^{\\circ}&=&68^{\\circ}&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  10. \\(\\begin{array}{rrrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nA_1&=&A_2&&&&&&&& \\\\\r\nA_3&=&A_1&-&12&&&&&& \\\\ \\\\\r\nA_1&+&A_2&+&A_3&&&=&180&& \\\\\r\nA_1&+&A_1&+&A_1&-&12&=&180&& \\\\\r\n&&&&&+&12&&+12&& \\\\\r\n\\midrule\r\n&&&&&&3A_1&=&192&& \\\\ \\\\\r\n&&&&&&A_1&=&\\dfrac{192}{3}&=&64 \\\\\r\nA_1&=&64^{\\circ}&&&&&&&& \\\\\r\nA_2&=&64^{\\circ}&&&&&&&& \\\\\r\nA_3&=&64^{\\circ}&-&12^{\\circ}&=&52^{\\circ}&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  11. \\(\\begin{array}{rrlrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nA_1&=&A_2&&&&&&&& \\\\\r\nA_3&=&3A_1&&&&&&&& \\\\ \\\\\r\nA_1&+&A_2&+&A_3&=&180&&&& \\\\\r\nA_1&+&A_1&+&3A_1&=&180&&&& \\\\\r\n&&&&5A_1&=&180&&&& \\\\ \\\\\r\n&&&&A_1&=&\\dfrac{180}{5}&=&36&& \\\\\r\nA_1&=&36^{\\circ}&&&&&&&& \\\\\r\nA_2&=&36^{\\circ}&&&&&&&& \\\\\r\nA_3&=&3(36^{\\circ})&=&108^{\\circ}&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  12. \\(\\begin{array}{rrrcrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nA_2&=&2A_1&&&&&&&& \\\\\r\nA_3&=&A_1&+&20&&&&&& \\\\ \\\\\r\nA_1&+&A_2&+&A_3&&&=&180&& \\\\\r\nA_1&+&2A_1&+&A_1&+&20&=&180&& \\\\\r\n&&&&&-&20&=&-20&& \\\\\r\n\\midrule\r\n&&&&&&4A_1&=&160&& \\\\ \\\\\r\n&&&&&&A_1&=&\\dfrac{160}{4}&=&40 \\\\\r\nA_1&=&40^{\\circ}&&&&&&&& \\\\\r\nA_2&=&2(40^{\\circ})&=&80^{\\circ}&&&&&& \\\\\r\nA_3&=&20^{\\circ}&+&40^{\\circ}&=&60^{\\circ}&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  13. \\(\\begin{array}{rrlllrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n^{\\text{1}}L&=&W&+&15&& \\\\ \\\\\r\n^{\\text{2}}P&=&2L&+&2W&& \\\\\r\n150&=&2(W&+&15)&+&2W \\\\\r\n150&=&2W&+&30&+&2W \\\\\r\n-30&&&-&30&& \\\\\r\n\\midrule\r\n120&=&4W&&&& \\\\ \\\\\r\nW&=&\\dfrac{120}{4}&=&30\\text{ cm}&& \\\\ \\\\\r\n^{\\text{3}}L&=&30&+&15&& \\\\\r\nL&=&45\\text{ cm}&&&& \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrlllrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n^{\\text{1}}L&=&W&+&40&& \\\\ \\\\\r\n^{\\text{2}}P&=&2L&+&2W&& \\\\\r\n304&=&2(W&+&40)&+&2W \\\\\r\n304&=&2W&+&80&+&2W \\\\\r\n-80&&&-&80&& \\\\\r\n\\midrule\r\n224&=&4W&&&& \\\\ \\\\\r\nW&=&\\dfrac{224}{4}&=&56\\text{ cm}&& \\\\ \\\\\r\n^{\\text{3}}L&=&56&+&40&& \\\\\r\nL&=&96\\text{ cm}&&&& \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{rrlllrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n^{\\text{1}}W&=&L&-&22&& \\\\ \\\\\r\n^{\\text{2}}P&=&2L&+&2W&& \\\\\r\n152&=&2L&+&2(L&-&22) \\\\\r\n152&=&2L&+&2L&-&44 \\\\\r\n+44&&&&&+&44 \\\\\r\n\\midrule\r\n196&=&4L&&&& \\\\ \\\\\r\nL&=&\\dfrac{196}{4}&=&49\\text{ m}&& \\\\ \\\\\r\n^{\\text{3}}W&=&49&-&22&& \\\\\r\nL&=&27\\text{ m}&&&& \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  16. \\(\\begin{array}{rrlllrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n^{\\text{1}}W&=&L&-&26&& \\\\ \\\\\r\n^{\\text{2}}P&=&2L&+&2W&& \\\\\r\n280&=&2L&+&2(L&-&26) \\\\\r\n280&=&2L&+&2L&-&52 \\\\\r\n+52&&&&&+&52 \\\\\r\n\\midrule\r\n332&=&4L&&&& \\\\ \\\\\r\nL&=&\\dfrac{332}{4}&=&83\\text{ m}&& \\\\ \\\\\r\n^{\\text{3}}W&=&83&-&26&& \\\\\r\nL&=&57\\text{ m}&&&& \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  17. \\(\\begin{array}{rrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\nx&+&2x&=&12&&& \\\\\r\n&&3x&=&12&&& \\\\ \\\\\r\n&&x&=&\\dfrac{12}{3}&=&4\\text{ cm}& \\\\ \\\\\r\n&\\therefore &2x&=&2(4)&=&8\\text{ cm}& \\\\\r\n\\end{array}\\)\\(\\text{Pieces are 4 cm and 8 cm}\\)\r\n\r\n\"\"<\/li>\r\n \t
  18. \\(\\begin{array}{rrrrrrrrcrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nx&+&x&+&2&=&30&&&& \\\\\r\n&&&-&2&&-2&&&& \\\\\r\n\\midrule\r\n&&&&2x&=&28&&&& \\\\ \\\\\r\n&&&&x&=&\\dfrac{28}{2}&=&14\\text{ m}&& \\\\ \\\\\r\n&\\therefore &x&+&2&=&14&+&2&=&16 \\text{ m}\r\n\\end{array}\\)\\(\\text{Pieces are 14 m and 16 m}\\)\r\n\r\n\"\"<\/li>\r\n<\/ol>","rendered":"
      \n
    1. \"L=2W-3 \text{ and } P=2L+2W \Rightarrow 54=2(2W-3)+2W\"<\/li>\n
    2. \"L=2W-8 \text{ and } P=2L+2W \Rightarrow 64=2(2W-8)+2W\"<\/li>\n
    3. \"L=2W+4 \text{ and } P=2L+2W \Rightarrow 32=2(2W+4)+2W\"<\/li>\n
    4. \"A_1=2A_2, A_1=10^{\circ}+A_3, A_1+A_2+A_3=180^{\circ} \Rightarrow\"
      \n\"A_1+\dfrac{A_1}{2}+A_1- 10^{\circ}=180^{\circ}\"<\/li>\n
    5. \"A_1=\dfrac{1}{2}A_2, A_1=20^{\circ}+A_3, A_1+A_2+A_3=180^{\circ} \Rightarrow\"
      \n\"A_1+2A_1+A_1-20^{\circ}=180^{\circ}\"<\/li>\n
    6. \"A_1+A_2=\dfrac{1}{2}A_3, A_1+A_2+A_3=180^{\circ} \Rightarrow\"
      \n\"\dfrac{3}{2}A_3=180^{\circ}\hspace{0.34in} A_1 \text{ and } A_2?\"<\/li>\n
    7. \"x_1+x_2=140, x_1=5x_2 \Rightarrow 5x_2+x_2=140\"<\/li>\n
    8. \"x_1+x_2=48, x_2=5+x_1 \Rightarrow x_1+5+x_1=48\"<\/li>\n
    9. \"\begin{array}{rrrrrrrrrrrrr}<\/li>\n
    10. \"\begin{array}{rrrrrrrrrrr}<\/li>\n
    11. \"\begin{array}{rrlrrrrrrrr}<\/li>\n
    12. \"\begin{array}{rrrcrrrrrrr}<\/li>\n
    13. \"\begin{array}{rrlllrr}<\/li>\n
    14. \"\begin{array}{rrlllrr}<\/li>\n
    15. \"\begin{array}{rrlllrr}<\/li>\n
    16. \"\begin{array}{rrlllrr}<\/li>\n
    17. \"\begin{array}{rrrrrrrr}\"\text{Pieces are 4 cm and 8 cm}\"\n

      \"\"<\/li>\n

    18. \"\begin{array}{rrrrrrrrcrr}\"\text{Pieces are 14 m and 16 m}\"\n

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