document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=130770>Question 130770</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The flower garden has the shape of a right triangle.  20 ft. of a perennial border forms the hypotenuse of the triangle, and one leg is 4 ft longer than the other leg.  Find the lengths of the legs.\r<BR>\n" );
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document.write( "I was trying to set up using the pythagorean theorem and for some reason my answers keeps coming up as incorrect.\r<BR>\n" );
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document.write( "Setting up the problem as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%5E2+=+x%5E2+%2B+%28x+%2B+4%29%5E2 ALIGN=MIDDLE  ALT=\"20%5E2+=+x%5E2+%2B+%28x+%2B+4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Am I doing something wrong? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #95479 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=95479\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%5E2+=+x%5E2+%2B+%28x+%2B+4%29%5E2 ALIGN=MIDDLE  ALT=\"20%5E2+=+x%5E2+%2B+%28x+%2B+4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > looks mighty good to me.  Let's see where this takes us:\r<BR>\n" );
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document.write( "I'll start by turning things around:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28x+%2B+4%29%5E2=20%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28x+%2B+4%29%5E2=20%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Expand and collect terms:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B8x%2B16=400 ALIGN=MIDDLE  ALT=\"2x%5E2%2B8x%2B16=400\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Put in standard form (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B8x%2B16-400=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B8x%2B16-400=0\"   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=2x%5E2%2B8x-384=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B8x-384=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide by the lead coefficient to get things in lowest terms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x-192=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x-192=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Finally, factor the trinomial (or complete the square, or use the quadratic formula, according to your preference):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-12%29%28x%2B16%29=0 ALIGN=MIDDLE  ALT=\"%28x-12%29%28x%2B16%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12%2A16=-192 ALIGN=MIDDLE  ALT=\"-12%2A16=-192\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12%2B16=4 ALIGN=MIDDLE  ALT=\"-12%2B16=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This says that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=12 ALIGN=MIDDLE  ALT=\"x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-16 ALIGN=MIDDLE  ALT=\"x=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but we can exclude the negative root for two reasons.  First, because we are looking for a measure of length, a negative number is absurd, and secondly, since in setting up the original equation you squared the variable, you introduced an extraneous root -- one that satisfies the derived equation, but does not satisfy the original problem.\r<BR>\n" );
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document.write( "Therefore, the correct answer is that the short leg is 12 feet and the long leg is 16 feet.\r<BR>\n" );
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document.write( "Check the answer:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%5E2=144 ALIGN=MIDDLE  ALT=\"12%5E2=144\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%5E2=256 ALIGN=MIDDLE  ALT=\"16%5E2=256\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144%2B256=400 ALIGN=MIDDLE  ALT=\"144%2B256=400\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28400%29=20 ALIGN=MIDDLE  ALT=\"sqrt%28400%29=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Answer checks. </SPAN>\n" );
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