document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=36209>Question 36209</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help!  Submitted question earlier didn't get a response.\r<BR>\n" );
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document.write( "4)	Amanda has 400 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). She wants to maximize the area of her patio (area of a rectangle is length times width). What should the dimensions of the patio be, and show how the maximum area of the patio is calculated from the algebraic equation.\r<BR>\n" );
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document.write( "Answer:  <BR>\n" );
document.write( "Show work in this space.  \r<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 #22181 by </B><A HREF=/tutors/aboutme.mpl?userid=Prithwis><B>Prithwis(166)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Prithwis><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.nriassociation.com/BeliveITorNOT/mittal70millionHouse.jpg valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=22181\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the length of the rectangular patio be x ft<BR>\n" );
document.write( "Perimeter of the rectangular patio = 400 ft <BR>\n" );
document.write( "The width of the rectangular patio would be 1/2(400-2x) = 200-x<BR>\n" );
document.write( "Area = Length * Width = x(200-x)<BR>\n" );
document.write( "We need to maximize f(x) = x(200-x) to achieve the goal of the problem.<BR>\n" );
document.write( "f(x) is quadratic function for Area, which represents a parabola opening downward (because the co-efficient of x^2 is negative).<BR>\n" );
document.write( "Maximum of f(x) is reached at the vertex (because it opens downward)<BR>\n" );
document.write( "x-Coordinate of the vertex = -b/2a (for ax^2+bx+c);<BR>\n" );
document.write( "f(x) = -x^2+200x; So, a = -1, b=200, c=0<BR>\n" );
document.write( "(-b/2a) = 100;<BR>\n" );
document.write( "So, maximum area can be obtained if the length is 100 feet;<BR>\n" );
document.write( "The width will be 1/2(400-200) = 100 feet;<BR>\n" );
document.write( "Answer - Dimension of the patio for maximum area will be 100 feet X 100 feet\r<BR>\n" );
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