document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087451>Question 1087451</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the rectangle of perimeter l which has the maximum area </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #701745 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=701745\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Max area is when the rectangle is a square:  L=W= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%281%2F4%29+ ALIGN=MIDDLE  ALT=\"+highlight%281%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "—\r<BR>\n" );
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document.write( "Proof:   2L + 2W = 1  —> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+W=%281-2L%29%2F2+ ALIGN=MIDDLE  ALT=\"+W=%281-2L%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "             A = LW = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L%281-2L%29%2F2++=+%281%2F2%29%28L-2L%5E2%29+ ALIGN=MIDDLE  ALT=\"+L%281-2L%29%2F2++=+%281%2F2%29%28L-2L%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take derivative of A with respect to L:<BR>\n" );
document.write( "             dA/dL = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F2%29%281-4L%29+ ALIGN=MIDDLE  ALT=\"+%281%2F2%29%281-4L%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Set that to 0 and solve for L, while noting that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2A%2FdL%5E2+=+-2+ ALIGN=MIDDLE  ALT=\"d%5E2A%2FdL%5E2+=+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > —> Concave down so our answer will give us a MAX:<BR>\n" );
document.write( "                  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F2%29%281-4L%29+=+0+ ALIGN=MIDDLE  ALT=\"+%281%2F2%29%281-4L%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "                  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+++4L+=+1+ ALIGN=MIDDLE  ALT=\"+++4L+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "                   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++L+=+1%2F4+ ALIGN=MIDDLE  ALT=\"++L+=+1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  —>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+W+=+1%2F4+ ALIGN=MIDDLE  ALT=\"+W+=+1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >   <BR>\n" );
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document.write( "              Since L=W we have a square.\r<BR>\n" );
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