document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189349>Question 189349</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A farmer has 500 feet of fencing to use to make a rectangular garden.  One side of the garden will be a barn, which requires no fencing.  How should the pen be built in order to enclose the largest amount of area possible?\r<BR>\n" );
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document.write( "Give your answer by filling in the blanks in the following sentence:   The farmer should build the pen ______ feet away from the barn, and ________ feet wide, for an area of _______ square feet<BR>\n" );
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document.write( "How do I solve this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142123 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=142123\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A farmer has 500 feet of fencing to use to make a rectangular garden.<BR>\n" );
document.write( " One side of the garden will be a barn, which requires no fencing.<BR>\n" );
document.write( " How should the pen be built in order to enclose the largest amount of area possible?<BR>\n" );
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document.write( "Let L = the length<BR>\n" );
document.write( "Let x = the width<BR>\n" );
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document.write( "We only need 3 sides so the perimeter equation would be:<BR>\n" );
document.write( "L + 2x = 500<BR>\n" );
document.write( "L = (500-2x)<BR>\n" );
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document.write( "Area = x * L<BR>\n" );
document.write( "Substitute (500-2x) for L<BR>\n" );
document.write( "A = x(500-2x)<BR>\n" );
document.write( "A = -2x^2 + 500x<BR>\n" );
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document.write( "A quadratic equation, we can use the axis of symmetry and vertex to find the maximum area; <BR>\n" );
document.write( "x = -500/(2*-2)<BR>\n" );
document.write( "x = -500/-4<BR>\n" );
document.write( "x = 125 ft is the width which will give max area<BR>\n" );
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document.write( "The length:<BR>\n" );
document.write( "L = 500 - 2(125)<BR>\n" );
document.write( "L = 250 ft is the length for max area<BR>\n" );
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document.write( "Find the max area<BR>\n" );
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document.write( "A = 250 * 125<BR>\n" );
document.write( "A = 31,250 sq/ft<BR>\n" );
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document.write( "I'll let you fill in the blanks<BR>\n" );
document.write( "\"The farmer should build the pen ______ feet away from the barn, and ________ <BR>\n" );
document.write( "feet wide, for an area of _______ square feet </SPAN>\n" );
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