document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=258860>Question 258860</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You have 500 ft of fencing all rolled up and you want to make a rectangular playground area for your son. What are the dimensions of the largest playground you could build? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #190579 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=190579\">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=A=L%2AW ALIGN=MIDDLE  ALT=\"A=L%2AW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For a rectangle, the perimeter is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=2%2A%28L%2BW%29=500 ALIGN=MIDDLE  ALT=\"P=2%2A%28L%2BW%29=500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2BW=250 ALIGN=MIDDLE  ALT=\"L%2BW=250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=250-W ALIGN=MIDDLE  ALT=\"L=250-W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute this into the area equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28250-W%29W=250W-W%5E2 ALIGN=MIDDLE  ALT=\"A=%28250-W%29W=250W-W%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To find the maximium area, take the derivative and set it to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2FdW=250-2W=0 ALIGN=MIDDLE  ALT=\"dA%2FdW=250-2W=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d2A%2Fdw2=-2 ALIGN=MIDDLE  ALT=\"d2A%2Fdw2=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > so you know that the value you get is a maximum (2nd derivative test).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250-2W=0 ALIGN=MIDDLE  ALT=\"250-2W=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2W=250 ALIGN=MIDDLE  ALT=\"+2W=250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=125 ALIGN=MIDDLE  ALT=\"W=125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=250-W=125 ALIGN=MIDDLE  ALT=\"L=250-W=125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The rectangle with the most area is actually a 125' x 125' square.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );