document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211581>Question 211581</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A banner in the shape of an isosceles triangle has a base that is 2 inches shorter than either of the equal sides. If the perimeter of the banner is 43 inches, then what is the length of the equal sides?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #159865 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=159865\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Recall that the perimeter of any triangle is\r<BR>\n" );
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document.write( "P = length of side1 + length of side2 + length of side3\r<BR>\n" );
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document.write( "Now let\r<BR>\n" );
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document.write( "x = length of side1<BR>\n" );
document.write( "y = length of side2<BR>\n" );
document.write( "z = length of side3\r<BR>\n" );
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document.write( "So the perimeter is now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=x%2By%2Bz ALIGN=MIDDLE  ALT=\"P=x%2By%2Bz\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Because the triangle is an isosceles, there are two sides that are equal. So let's make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=z ALIGN=MIDDLE  ALT=\"y=z\"   DISABLED_style= \"max-width:90%; height:auto;\" > which will make the base be 'x'. Since the \"triangle has a base that is 2 inches shorter than either of the equal sides\", this means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y-2 ALIGN=MIDDLE  ALT=\"x=y-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=z-2 ALIGN=MIDDLE  ALT=\"x=z-2\"   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=P=x%2By%2Bz ALIGN=MIDDLE  ALT=\"P=x%2By%2Bz\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=43=z-2%2Bz%2Bz ALIGN=MIDDLE  ALT=\"43=z-2%2Bz%2Bz\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=43 ALIGN=MIDDLE  ALT=\"P=43\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the given perimeter), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=z-2 ALIGN=MIDDLE  ALT=\"x=z-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=z ALIGN=MIDDLE  ALT=\"y=z\"   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=43=3z-2 ALIGN=MIDDLE  ALT=\"43=3z-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=43%2B2=3z ALIGN=MIDDLE  ALT=\"43%2B2=3z\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45=3z ALIGN=MIDDLE  ALT=\"45=3z\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2845%29%2F3=z ALIGN=MIDDLE  ALT=\"%2845%29%2F3=z\"   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=z ALIGN=MIDDLE  ALT=\"z\"   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=15=z ALIGN=MIDDLE  ALT=\"15=z\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=15 ALIGN=MIDDLE  ALT=\"z=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation.\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=z ALIGN=MIDDLE  ALT=\"y=z\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=15 ALIGN=MIDDLE  ALT=\"y=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > also. So the length of the equal sides is 15 inches. Subtract 2 from this to get 13\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the triangle has side lengths of 13, 15, and 15 inches\r<BR>\n" );
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