document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=381586>Question 381586</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that you have 800ft of fencing. you are to constuct a rectangular corral which is divided into two pieces. What are the dimensions that give the largest possible area?\r<BR>\n" );
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document.write( "First, Construct a quadratic function that gives the area of the enclosure in terms of a single variable?<BR>\n" );
document.write( "I can't figure out the quadratic equation to use. I tried 2y^2 + 3x=0 but of course did not work. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #270669 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=270669\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose that you have 800ft of fencing. you are to constuct a rectangular corral which is divided into two pieces. What are the dimensions that give the largest possible area? <BR>\n" );
document.write( "First, Construct a quadratic function that gives the area of the enclosure in terms of a single variable?<BR>\n" );
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document.write( "Draw the picture: a rectangle with a segment parallel to a side  dividing the area.<BR>\n" );
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document.write( "Let the dividing segment have length \"x\". (Note there are 3 segments of <BR>\n" );
document.write( "length \"x\")<BR>\n" );
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document.write( "800-3x is the remaining fence length.<BR>\n" );
document.write( "(800-3x) is the length of the base and of the top of the rectangle.<BR>\n" );
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document.write( "Area of the outer rectangle is x(800-3x)/2<BR>\n" );
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document.write( "Simplify that Area Equation:<BR>\n" );
document.write( "A(x) = (-3/2)x^2+ 400x<BR>\n" );
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document.write( "That is a quadratic with a = -3/2 and b = 400<BR>\n" );
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document.write( "Maximum area occurs when x = -b/2a = -400(2(-3/2)) = 400/3 = 133 1/3 ft.<BR>\n" );
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document.write( "Dimensions of the corral are:<BR>\n" );
document.write( "height = x = 133 1/3 ft<BR>\n" );
document.write( "width: = (800-3x)/2 = (800-3(400/3))/2 = 200 ft<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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