document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=581762>Question 581762</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a farmer has 1000m of fencing to enclose a rectangular<BR>\n" );
document.write( "field. What is the largest area that the farmer can enclose? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #371796 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=371796\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The Perimeter is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+2W+%2B+2L+ ALIGN=MIDDLE  ALT=\"+P+=+2W+%2B+2L+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1000+=+2W+%2B+2L+ ALIGN=MIDDLE  ALT=\"+1000+=+2W+%2B+2L+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+=+W+%2B+L+ ALIGN=MIDDLE  ALT=\"+500+=+W+%2B+L+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+=+500+-+W+ ALIGN=MIDDLE  ALT=\"+L+=+500+-+W+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "The Area is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+W%2AL+ ALIGN=MIDDLE  ALT=\"+A+=+W%2AL+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+W%2A%28+500+-+W+%29+ ALIGN=MIDDLE  ALT=\"+A+=+W%2A%28+500+-+W+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+-W%5E2+%2B+500W+ ALIGN=MIDDLE  ALT=\"+A+=+-W%5E2+%2B+500W+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "First of all, when the coefficient of the<BR>\n" );
document.write( "squared term is negative, then there is a maximum<BR>\n" );
document.write( "and not a minimum.<BR>\n" );
document.write( "When the equation is in the form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+ax%5E2+%2B+ba+%2B+c+ ALIGN=MIDDLE  ALT=\"+y+=+ax%5E2+%2B+ba+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the max or min is<BR>\n" );
document.write( "always at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+x+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or, in this case,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+W%5Bmax%5D+=+-500%2F%282%2A%28-1%29%29+ ALIGN=MIDDLE  ALT=\"+W%5Bmax%5D+=+-500%2F%282%2A%28-1%29%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%5Bmax%5D+=+250+ ALIGN=MIDDLE  ALT=\"+W%5Bmax%5D+=+250+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and I know that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+=+500+-+W+ ALIGN=MIDDLE  ALT=\"+L+=+500+-+W+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L%5Bmax%5D+=+500+-+250+ ALIGN=MIDDLE  ALT=\"+L%5Bmax%5D+=+500+-+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%5Bmax%5D+=+250+ ALIGN=MIDDLE  ALT=\"+L%5Bmax%5D+=+250+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The largest area that the farmer can enclose<BR>\n" );
document.write( "is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+250%2A250+ ALIGN=MIDDLE  ALT=\"+250%2A250+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 62,500 ft2<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "I can prove this by changing the dimensions<BR>\n" );
document.write( "slightly, but still keeping the same Perimeter<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+249%2A251+ ALIGN=MIDDLE  ALT=\"+249%2A251+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 62,499 ft2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+248%2A252+ ALIGN=MIDDLE  ALT=\"+248%2A252+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 62,496 ft2 ( even less ) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );