document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=162680>Question 162680</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A homeowner wants to fence a rectangular garden using 120ft of fencing.  The side of the garage will be used as one side of the rectangle.  Find the dimension for which the area is a maximum.<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 #119899 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=119899\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let w = width<BR>\n" );
document.write( "and L = length<BR>\n" );
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document.write( "then:<BR>\n" );
document.write( "2w + L = 120  (equation 1)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "area = wL (equation 2)<BR>\n" );
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document.write( "Solve for L in equation 1:<BR>\n" );
document.write( "2w + L = 120<BR>\n" );
document.write( "L = 120-2w<BR>\n" );
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document.write( "Substitute the above into equation 2:<BR>\n" );
document.write( "area = wL<BR>\n" );
document.write( "area = w(120-2w)<BR>\n" );
document.write( "area = 120w-2w^2<BR>\n" );
document.write( "area = -2w^2+120w<BR>\n" );
document.write( "area = -2(w^2-60w)<BR>\n" );
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document.write( "The standard parabola equation is:<BR>\n" );
document.write( "y= a(x-h)2+k<BR>\n" );
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document.write( "Strategy is manipulate the equation so that it fits that form (to find the vertex) -- do this by completing the square:<BR>\n" );
document.write( "area = -2(w^2-60w)<BR>\n" );
document.write( "area = -2(w^2-60w+900)+1800<BR>\n" );
document.write( "area = -2(w-30)^2+1800<BR>\n" );
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document.write( "(h,k) is the vertex:<BR>\n" );
document.write( "(30,1800)<BR>\n" );
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document.write( "Therefore, area is maximized when<BR>\n" );
document.write( "w = 30 feet (width)<BR>\n" );
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document.write( "to find the length, we said the length is:<BR>\n" );
document.write( "L = 120-2w<BR>\n" );
document.write( "L = 120-2(30)<BR>\n" );
document.write( "L = 120-60<BR>\n" );
document.write( "L = 60 feet (length)<BR>\n" );
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document.write( "Conclusion:<BR>\n" );
document.write( "dimension is 30 by 60 feet rectangle </SPAN>\n" );
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