document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=657795>Question 657795</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider a rectangle that has a diagonal of 20 feet and a perimeter of 52 feet. Find the area of this rectangle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #410032 by </B><A HREF=/tutors/aboutme.mpl?userid=kevwill><B>kevwill(135)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kevwill><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=kevwill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=410032\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let l be the length of the rectangle and w be the width of the rectangle.  With the diagonal being 20 feet long, using the Pythagorean Theormem, we get <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28l%5E2+%2B+w%5E2%29+=+20 ALIGN=MIDDLE  ALT=\"sqrt%28l%5E2+%2B+w%5E2%29+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l%5E2+%2B+w%5E2+=+400 ALIGN=MIDDLE  ALT=\"l%5E2+%2B+w%5E2+=+400\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "With a perimeter of 52 feet, we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Al+%2B+2%2Aw+=+52 ALIGN=MIDDLE  ALT=\"2%2Al+%2B+2%2Aw+=+52\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l+%2B+w+=+26 ALIGN=MIDDLE  ALT=\"l+%2B+w+=+26\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l+=+26+-+w ALIGN=MIDDLE  ALT=\"l+=+26+-+w\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substituting, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2826-w%29%5E2+%2B+w%5E2+=+400 ALIGN=MIDDLE  ALT=\"%2826-w%29%5E2+%2B+w%5E2+=+400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28676-52w%2Bw%5E2%29+%2B+w%5E2+=+400 ALIGN=MIDDLE  ALT=\"%28676-52w%2Bw%5E2%29+%2B+w%5E2+=+400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aw%5E2+-+52w+%2B+276+=+0 ALIGN=MIDDLE  ALT=\"2%2Aw%5E2+-+52w+%2B+276+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We can solve for w using the quadratic equation with a=2, b=-52, and c=276:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-%28-52%29+%2B-+sqrt%28+%28-52%29%5E2-4%2A2%2A276%29%29%2F%282%2A2%29+ ALIGN=MIDDLE  ALT=\"w+=+%28-%28-52%29+%2B-+sqrt%28+%28-52%29%5E2-4%2A2%2A276%29%29%2F%282%2A2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%2852+%2B-+sqrt%282704-2208%29%29+%2F+4+=+%2852+%2B-+sqrt%2816%2A31%29%29%2F4+=+%2852+%2B-+4sqrt%2831%29%29%2F4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+13+%2B-+sqrt%2831%29+ ALIGN=MIDDLE  ALT=\"w+=+13+%2B-+sqrt%2831%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+13+%2B+sqrt%2831%29+ ALIGN=MIDDLE  ALT=\"+w+=+13+%2B+sqrt%2831%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+l+=+26-w+=+26+-+%2813%2Bsqrt%2831%29%29+=+13-sqrt%2831%29+ ALIGN=MIDDLE  ALT=\"+l+=+26-w+=+26+-+%2813%2Bsqrt%2831%29%29+=+13-sqrt%2831%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+13+-+sqrt%2831%29+ ALIGN=MIDDLE  ALT=\"+w+=+13+-+sqrt%2831%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+l+=+26-w+=+26+-+%2813-sqrt%2831%29%29+=+13%2Bsqrt%2831%29+ ALIGN=MIDDLE  ALT=\"+l+=+26-w+=+26+-+%2813-sqrt%2831%29%29+=+13%2Bsqrt%2831%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Both of these are basically the same solution with the l and w values being switched.  So the area is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+l+%2A+w+=+%2813%2Bsqrt%2831%29%29%2A%2813-sqrt%2831%29%29+=+169%2B13sqrt%2831%29-13sqrt%2831%29-%28sqrt%2831%29%29%5E2+=+169+-+31+=+138 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The area is 138 square feet.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
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