document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=530159>Question 530159</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer has 5000 feet of fencing available to enclose a rectangular field. What is the maximum area? \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 #349941 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=349941\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For any given perimeter, the maximum area is a square.<BR>\n" );
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document.write( "5000/4 = 1250<BR>\n" );
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document.write( "1250^2 = 1562500 sq. ft.<BR>\n" );
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document.write( "If you're not familiar with the maximum area rectangle being a square, a simple application of calculus will demonstrate.<BR>\n" );
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document.write( "Recall, perimeter = 2(length +  width).  With 5000 feet of fencing, that is the maximum perimeter.<BR>\n" );
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document.write( "From this starting point, we recognize that 1/2 the perimeter equals the rectangle's length + its width.<BR>\n" );
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document.write( "5000/2 = 2500<BR>\n" );
document.write( "so<BR>\n" );
document.write( "L + W = 2500<BR>\n" );
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document.write( "So the sides can be defined as 'L = x' and 'W = 2500-x'.<BR>\n" );
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document.write( "y = area = L*W<BR>\n" );
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document.write( "Substitute for L and W.<BR>\n" );
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document.write( "y = x*(2500-x)<BR>\n" );
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document.write( "y = -x^2 + 2500x<BR>\n" );
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document.write( "To find the maximum, take the first derivative and solve it for a value of 0.<BR>\n" );
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document.write( "dy/dx = -2x + 2500<BR>\n" );
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document.write( "2x = 2500<BR>\n" );
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document.write( "x = 1250 = L<BR>\n" );
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document.write( "2500-x = 1250 = W<BR>\n" );
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document.write( "L = W, so we have a square.<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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