document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=888586>Question 888586</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer wants to fence in three sides of a rectangular field with 1000 feet of fencing. The other side of the rectangle is a river. If the enclosed area is to be maximum, find the dimensions of the field.\r<BR>\n" );
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document.write( "Now I was able to get the area, if I am right, I think the area is 125,000 feet. How do I get the dimensions?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #537483 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=537483\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> L = length<BR>\n" );
document.write( "W = width<BR>\n" );
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document.write( "Perimeter is normally equal to 2L + 2W, but you are missing 1 side.<BR>\n" );
document.write( "We'll assume it's the length.\r<BR>\n" );
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document.write( "since you have 1000 feet of fencing, then L + 2W = 1000\r<BR>\n" );
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document.write( "solve for L to get:\r<BR>\n" );
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document.write( "L = 1000 - 2W\r<BR>\n" );
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document.write( "area is equal to L*W\r<BR>\n" );
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document.write( "replace L with 1000 - 2W to get:\r<BR>\n" );
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document.write( "area = (1000 - 2W) * W\r<BR>\n" );
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document.write( "simplify this to get:\r<BR>\n" );
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document.write( "area = 1000W - 2W^2\r<BR>\n" );
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document.write( "this is a quadratic equation, so convert it to standard form to get:\r<BR>\n" );
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document.write( "area = -2W^2 + 1000W\r<BR>\n" );
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document.write( "replace W with x to get:\r<BR>\n" );
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document.write( "area = -2x^2 + 1000x\r<BR>\n" );
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document.write( "since it's in standard form of y = ax^2 + bx + c:\r<BR>\n" );
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document.write( "a = -2<BR>\n" );
document.write( "b = 1000<BR>\n" );
document.write( "c = 0\r<BR>\n" );
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document.write( "since the coefficient of the x^2 term is negative, this will have a maximum.\r<BR>\n" );
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document.write( "the maximum point will be at x = -b/(2a) = -1000 / -4 = 250.\r<BR>\n" );
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document.write( "the equation will be at a maximum when x = 250\r<BR>\n" );
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document.write( "when x = 250, -2x^2 + 1000x = -2(250)^2 + 1000(250) = 125000.\r<BR>\n" );
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document.write( "since x represents W which represents the width, then W = 250.\r<BR>\n" );
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document.write( "since area is L * W, then L * 250 = 125000.\r<BR>\n" );
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document.write( "solve for L to get L = 125000 / 250 = 500\r<BR>\n" );
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document.write( "the length is 500 and the width is 250.\r<BR>\n" );
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document.write( "the area is 500 * 250 = 125000\r<BR>\n" );
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document.write( "the perimeter for fencing is L + 2W = 500 + 2(250) = 500 + 500 = 1000\r<BR>\n" );
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document.write( "all is good.<BR>\n" );
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