document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174569>Question 174569</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is one is tough!  <BR>\n" );
document.write( "A rectangular enclosure is made with 100 ft. of fencing on three sides.  The fourth side is the wall of a barn.  Find the greatest possible area of such an enclosure.  My choices are as follows: A) 400ft^2 B) 625 ft^2  C) 1111.1 ft ^2  D) 2500ft^2. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129585 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=129585\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you only have 100 feet of fencing, this means that the perimeter has a maximum of 100 feet.<BR>\n" );
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document.write( "Let x = width<BR>\n" );
document.write( "and y = length<BR>\n" );
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document.write( "Perimeter = 2x+y<BR>\n" );
document.write( "100 = 2x+y<BR>\n" );
document.write( "solving for y:<BR>\n" );
document.write( "y = 100 - 2x<BR>\n" );
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document.write( "Area = xy<BR>\n" );
document.write( "substituting in our value of y:<BR>\n" );
document.write( "Area = x(100 - 2x)<BR>\n" );
document.write( "Area = -2x^2 + 100x<BR>\n" );
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document.write( "This is essentially a parabola that opens downward (from the coefficient -2).  So, all we need to do is to find the vertex to find the maximum.<BR>\n" );
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document.write( "The x coordinate = -b/2a<BR>\n" );
document.write( "The x coordinate = -(100)/2(-2)<BR>\n" );
document.write( "The x coordinate = (-100)/(-4)<BR>\n" );
document.write( "The x coordinate = (100)/(4)<BR>\n" );
document.write( "The x coordinate = 25 feet (width)<BR>\n" );
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document.write( "Length is:<BR>\n" );
document.write( "y = 100 - 2x<BR>\n" );
document.write( "y = 100 - 2(25)<BR>\n" );
document.write( "y = 100 - 50<BR>\n" );
document.write( "y = 50 feet (length)<BR>\n" );
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document.write( "Area is then:<BR>\n" );
document.write( "25(50) = 1250 square feet\r<BR>\n" );
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document.write( " </SPAN>\n" );
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