document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=670274>Question 670274</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a woman has 40 yards of fencing for her yard. what is the maximum area she can enclose? this has to be extended response.. please help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #416849 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=416849\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I already know that the maximum area is<BR>\n" );
document.write( "when the yard is a square, but I will prove this.<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+ ALIGN=MIDDLE  ALT=\"+L+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the length of a rectangular yard<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+W+ ALIGN=MIDDLE  ALT=\"+W+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the width of this rectangular yard<BR>\n" );
document.write( "given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2L+%2B+2W+=+40+ ALIGN=MIDDLE  ALT=\"+2L+%2B+2W+=+40+\"   DISABLED_style= \"max-width:90%; height:auto;\" > yds<BR>\n" );
document.write( "( this is the definition of circumference of a rectangle )<BR>\n" );
document.write( "Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+ ALIGN=MIDDLE  ALT=\"+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+%2B+W+=+20+ ALIGN=MIDDLE  ALT=\"+L+%2B+W+=+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+W+=+20+-+L+ ALIGN=MIDDLE  ALT=\"+W+=+20+-+L+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+ ALIGN=MIDDLE  ALT=\"+A+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the area of the yard<BR>\n" );
document.write( "(2) <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;\" > ( also a definition )<BR>\n" );
document.write( "substitute (1) into (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+L%2A%28+20+-+L+%29+ ALIGN=MIDDLE  ALT=\"+A+=+L%2A%28+20+-+L+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+-L%5E2+%2B+20L+ ALIGN=MIDDLE  ALT=\"+A+=+-L%5E2+%2B+20L+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "The rule is: when a quadratic equation has the form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the max ( or min ) occurs where<BR>\n" );
document.write( "the x-co-ordinate is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this problem,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-1+ ALIGN=MIDDLE  ALT=\"+a+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+20+ ALIGN=MIDDLE  ALT=\"+b+=+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+-20%2F%28-2%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+-20%2F%28-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+10+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+10+\"   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+=+10+ ALIGN=MIDDLE  ALT=\"+L%5Bmax%5D+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, since<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+%2B+W+=+20+ ALIGN=MIDDLE  ALT=\"+L+%2B+W+=+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10+%2B+W+=+20+ ALIGN=MIDDLE  ALT=\"+10+%2B+W+=+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+W+=+10+ ALIGN=MIDDLE  ALT=\"+W+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Both the length and width are 10, so this is a<BR>\n" );
document.write( "square yard<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+10%2A10+ ALIGN=MIDDLE  ALT=\"+A+=+10%2A10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+100+ ALIGN=MIDDLE  ALT=\"+A+=+100+\"   DISABLED_style= \"max-width:90%; height:auto;\" > square yards<BR>\n" );
document.write( "So, the maximum area is when all the sides are 10 yds<BR>\n" );
document.write( "Here's the plot with Area on the vertical axis<BR>\n" );
document.write( "and Length on the horizontal<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-5%2C+25%2C+-10%2C+110%2C++-x%5E2+%2B+20x+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-5%2C+25%2C+-10%2C+110%2C++-x%5E2+%2B+20x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );