document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1001420>Question 1001420</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Nicky has 120 feet of fence to put around a rectangular garden. if a 10 foot opening is left on one side for a gate. what would be the length and width for maximum area? L=20 ft w=20 ft </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #618604 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=618604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A square shape will give maximum area.  I do not give that analysis here.  The perimeter of this would be  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120%2B10 ALIGN=MIDDLE  ALT=\"120%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to include both the fence and the gate(unfenced).  Cut the 130 feet into four equal parts, and this is the side of the square garden.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32%261%2F2 ALIGN=MIDDLE  ALT=\"32%261%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet square.\r<BR>\n" );
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document.write( "MAXIMIZE AREA\r<BR>\n" );
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document.write( "Dimensions are x and y.<BR>\n" );
document.write( "The entire perimeter of the garden is length_of_fencing PLUS 10 feet for gate; so this means the perimeter of the garden is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120%2B10=130 ALIGN=MIDDLE  ALT=\"120%2B10=130\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet.\r<BR>\n" );
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document.write( "Two basic equations are needed.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%282x%2B2y=130%2CA=xy%2CA=AreaOfGarden%29 ALIGN=MIDDLE  ALT=\"system%282x%2B2y=130%2CA=xy%2CA=AreaOfGarden%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Use these to make a function A dependent on just ONE of the variables, either x or y.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2y=130 ALIGN=MIDDLE  ALT=\"2x%2B2y=130\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=65 ALIGN=MIDDLE  ALT=\"x%2By=65\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=65-x ALIGN=MIDDLE  ALT=\"y=65-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A=x%2865-x%29%29 ALIGN=MIDDLE  ALT=\"highlight%28A=x%2865-x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >------Area A is a function of the dimension, x, a quadratic function, and you can look for the MAXIMUM.  You know there is a maximum because the coefficient on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be negative...<BR>\n" );
document.write( "The max area will occur in the exact middle of the roots or zeros or x-intercepts of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28x%29 ALIGN=MIDDLE  ALT=\"A%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Solve for the x-intercepts.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28x%29=0=x%2865-x%29 ALIGN=MIDDLE  ALT=\"A%28x%29=0=x%2865-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The roots are 0 and 65.<BR>\n" );
document.write( "The value for x exactly in the middle is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%2B65%29%2F2=65%2F2=32%261%2F2 ALIGN=MIDDLE  ALT=\"%280%2B65%29%2F2=65%2F2=32%261%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "WHAT IS THE VALUE FOR y FOR THIS VALUE OF x ?<BR>\n" );
document.write( "WHAT IS THE AREA AT THIS VALUE OF x ? </SPAN>\n" );
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