document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=869209>Question 869209</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You have 180 yards of fencing to use on three sides of a garden. The fourth side is the tool shed.\r<BR>\n" );
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document.write( "a. What is the maximum area that you can fence?<BR>\n" );
document.write( "b. What are the dimensions of the garden? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #524250 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=524250\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the dimensions of the area be x-y-x where y is the length parallel to the tool shed.<BR>\n" );
document.write( "The area of the rectangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=xy ALIGN=MIDDLE  ALT=\"A=xy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The amount of fencing used is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=2x%2By=148 ALIGN=MIDDLE  ALT=\"L=2x%2By=148\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute into A,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=x%28148-2x%29=148x-2x%5E2 ALIGN=MIDDLE  ALT=\"A=x%28148-2x%29=148x-2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To maximize A, find the derivative of area with respect to x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fdx=148-4x=0 ALIGN=MIDDLE  ALT=\"dA%2Fdx=148-4x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=148 ALIGN=MIDDLE  ALT=\"4x=148\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=37 ALIGN=MIDDLE  ALT=\"x=37\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=148-2%2837%29 ALIGN=MIDDLE  ALT=\"y=148-2%2837%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=148-74 ALIGN=MIDDLE  ALT=\"y=148-74\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=74 ALIGN=MIDDLE  ALT=\"y=74\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So,<BR>\n" );
document.write( "a. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bmax%5D=37%2A74=2738 ALIGN=MIDDLE  ALT=\"A%5Bmax%5D=37%2A74=2738\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=37 ALIGN=MIDDLE  ALT=\"x=37\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=74 ALIGN=MIDDLE  ALT=\"y=74\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "If you had made a semi-circle with the fencing, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2AR=148 ALIGN=MIDDLE  ALT=\"pi%2AR=148\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=148%2Fpi ALIGN=MIDDLE  ALT=\"R=148%2Fpi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the area would have been<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%281%2F2%29pi%2AR%5E2 ALIGN=MIDDLE  ALT=\"A=%281%2F2%29pi%2AR%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >}<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%281%2F2%29pi%2A%28148%5E2%2Fpi%5E2%29 ALIGN=MIDDLE  ALT=\"A=%281%2F2%29pi%2A%28148%5E2%2Fpi%5E2%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=10952%2Fpi ALIGN=MIDDLE  ALT=\"A=10952%2Fpi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=3486 ALIGN=MIDDLE  ALT=\"A=3486\"   DISABLED_style= \"max-width:90%; height:auto;\" > a 27% increase in garden area using the same amount of fence.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );