document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=158174>Question 158174</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395771188/algebrahomeworkh>Algebra and Trigonometry: Structure and Method, book 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The three sides of an equilateral triangle are increased by 20 cm, 30 cm, and 40 cm, respectively.  The perimeter of the resulting triangle is between twice and three times the perimeter of the original triangle.  What can you conclude about the length of a side of the original triangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #116544 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=116544\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let s=length of side of equilateral triangle\r<BR>\n" );
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document.write( "So the perimeter of the equilateral triangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=s%2Bs%2Bs=3s ALIGN=MIDDLE  ALT=\"P=s%2Bs%2Bs=3s\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Because the sides \"are increased by 20 cm, 30 cm, and 40 cm\", this tells us that the new sides are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%2B20 ALIGN=MIDDLE  ALT=\"s%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%2B30 ALIGN=MIDDLE  ALT=\"s%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%2B40 ALIGN=MIDDLE  ALT=\"s%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "The perimeter of the new triangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=%28s%2B20%29%2B%28s%2B30%29%2B%28s%2B40%29=3s%2B90 ALIGN=MIDDLE  ALT=\"P=%28s%2B20%29%2B%28s%2B30%29%2B%28s%2B40%29=3s%2B90\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the \"perimeter of the resulting triangle is between twice and three times the perimeter of the original triangle\", this means that \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%283s%29%3C=3s%2B90%3C=3%283s%29 ALIGN=MIDDLE  ALT=\"2%283s%29%3C=3s%2B90%3C=3%283s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Note: remember, the term \"3s\" is the original perimeter\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6s%3C=3s%2B90%3C=9s ALIGN=MIDDLE  ALT=\"6s%3C=3s%2B90%3C=9s\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "Break up the compound inequality to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6s%3C=3s%2B90 ALIGN=MIDDLE  ALT=\"6s%3C=3s%2B90\"   DISABLED_style= \"max-width:90%; height:auto;\" > AND <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3s%2B90%3C=9s ALIGN=MIDDLE  ALT=\"3s%2B90%3C=9s\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So let's solve the first inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6s%3C=3s%2B90 ALIGN=MIDDLE  ALT=\"6s%3C=3s%2B90\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6s%3C=3s%2B90 ALIGN=MIDDLE  ALT=\"6s%3C=3s%2B90\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6s-3s%3C=90 ALIGN=MIDDLE  ALT=\"6s-3s%3C=90\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3s ALIGN=MIDDLE  ALT=\"3s\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3s%3C=90 ALIGN=MIDDLE  ALT=\"3s%3C=90\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%3C=%2890%29%2F%283%29 ALIGN=MIDDLE  ALT=\"s%3C=%2890%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s ALIGN=MIDDLE  ALT=\"s\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%3C=30 ALIGN=MIDDLE  ALT=\"s%3C=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "Now let's solve the second inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3s%2B90%3C=9s ALIGN=MIDDLE  ALT=\"3s%2B90%3C=9s\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3s%2B90%3C=9s ALIGN=MIDDLE  ALT=\"3s%2B90%3C=9s\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3s%3C=9s-90 ALIGN=MIDDLE  ALT=\"3s%3C=9s-90\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90 ALIGN=MIDDLE  ALT=\"90\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3s-9s%3C=-90 ALIGN=MIDDLE  ALT=\"3s-9s%3C=-90\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9s ALIGN=MIDDLE  ALT=\"9s\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6s%3C=-90 ALIGN=MIDDLE  ALT=\"-6s%3C=-90\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%3E=%28-90%29%2F%28-6%29 ALIGN=MIDDLE  ALT=\"s%3E=%28-90%29%2F%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s ALIGN=MIDDLE  ALT=\"s\"   DISABLED_style= \"max-width:90%; height:auto;\" >. note: Remember, the inequality sign flips when we divide both sides by a negative number. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%3E=15 ALIGN=MIDDLE  ALT=\"s%3E=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%3C=30 ALIGN=MIDDLE  ALT=\"s%3C=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > <b>and</b> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%3E=15 ALIGN=MIDDLE  ALT=\"s%3E=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Recombine the inequalities to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%3C=s%3C=30 ALIGN=MIDDLE  ALT=\"15%3C=s%3C=30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the side lengths of the original triangle are between 15 and 30 cm </SPAN>\n" );
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