document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=3405>Question 3405</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help:\r<BR>\n" );
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document.write( "Sue wants to put a rectangular garden on her property using 80 meters of fencing.  There is a river that runs through her property so she decides to increase the size of the garden by using the river as one side of the rectangle.  Fencing is then needed only on the other three sides.)  Let x represent the length of the side of the rectangle along the river.  Express the gardens area as a function of x.  Find the dimensions of the field so that its area is a maximum. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1486 by </B><A HREF=/tutors/aboutme.mpl?userid=pannalal><B>pannalal(9)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=pannalal><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=1486\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> As per question x represent the length of the side of the rectangle<BR>\n" );
document.write( "along the river. Let the width of garden be y.\r<BR>\n" );
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document.write( "The length of fence = x + 2y = 80\r<BR>\n" );
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document.write( "and the area of the garden = xy\r<BR>\n" );
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document.write( "We need to maximize the area of the garden.\r<BR>\n" );
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document.write( "Suppose x = 40+k where k is some constant either positive or negative\r<BR>\n" );
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document.write( "The equation for fencs is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+2y+=+80 ALIGN=MIDDLE  ALT=\"x+%2B+2y+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "On putting x = 40+k in the above equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2840%2Bk%29+%2B+2y+=+80 ALIGN=MIDDLE  ALT=\"%2840%2Bk%29+%2B+2y+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y+=+80-40-k ALIGN=MIDDLE  ALT=\"2y+=+80-40-k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+20-k%2F2 ALIGN=MIDDLE  ALT=\"y+=+20-k%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The area of garden is xy.\r<BR>\n" );
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document.write( "On putting the value of x and y in terms of k in area:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Area+=+%2840%2Bk%29%2A%2820-k%2F2%29 ALIGN=MIDDLE  ALT=\"Area+=+%2840%2Bk%29%2A%2820-k%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Area+=+800-k%5E2%2F2 ALIGN=MIDDLE  ALT=\"Area+=+800-k%5E2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To maximize the area, we need to take the value of k = 0.\r<BR>\n" );
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document.write( "Then, Area = 800 square meter\r<BR>\n" );
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document.write( "and x = 40 and y = 20.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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