document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1073354>Question 1073354</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 100m of wire is available for fencing a rectangular piece of land. find the dimension of land which maximize the area. hence, determine the maximum area of the fence. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #688183 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=688183\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 100m of wire is available for fencing a rectangular piece of land. find the <BR>\n" );
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document.write( "If the fence shape must be rectangular, then a square maximizes the enclosed area.\r<BR>\n" );
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document.write( "——  Proof that a square maximizes area ——\r<BR>\n" );
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document.write( " Perimeter = P = 2L + 2W <BR>\n" );
document.write( "   Area = A = L*W \r<BR>\n" );
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document.write( "A = ((P-2W)/2)*W =  (PW)/2 - W^2\r<BR>\n" );
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document.write( "dA/dW =  P/2 - 2W <BR>\n" );
document.write( "Set dA/dW = 0:   P/2 - 2W = 0  —>  W = P/4 —> L=P/4   so a square shape.<BR>\n" );
document.write( "——   End proof —————\r<BR>\n" );
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document.write( "A square with sides <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%2825m%29 ALIGN=MIDDLE  ALT=\"+highlight%2825m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > will maximize the area, and that area will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+25%5E2+=+625m%5E2 ALIGN=MIDDLE  ALT=\"+25%5E2+=+625m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "—————————————————  For fun/Info —————————————\r<BR>\n" );
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document.write( "To enclose the maximum area with no shape restrictions, a CIRCLE will do:  <BR>\n" );
document.write( "Circumference= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+=+2%28pi%29r+ ALIGN=MIDDLE  ALT=\"+C+=+2%28pi%29r+\"   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=+100+=+2%28pi%29r+ ALIGN=MIDDLE  ALT=\"+100+=+2%28pi%29r+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+100%2F%282%28pi%29%29+=+r+ ALIGN=MIDDLE  ALT=\"+100%2F%282%28pi%29%29+=+r+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+15.915m+=+r+ ALIGN=MIDDLE  ALT=\"+15.915m+=+r+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "—<BR>\n" );
document.write( "Making a circle with radius 15.915m would give you an enclosed area of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28pi%29r%5E2+=+795.725m%5E2+ ALIGN=MIDDLE  ALT=\"%28pi%29r%5E2+=+795.725m%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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