document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=53231>Question 53231</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4) 	John has 300 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). He wants to maximize the area of his 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( "	Show clearly the algebraic steps which prove your dimensions are the maximum area which can be obtained. Use the vertex form to find the maximum area.\r<BR>\n" );
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document.write( "Answer:	\r<BR>\n" );
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document.write( "Show work in this space. <BR>\n" );
document.write( "Thank You </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #35498 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=35498\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P=2L+2W<BR>\n" );
document.write( "Let the length =L<BR>\n" );
document.write( "We only want one variable, so plug 300 in for p and solve for W (your width).<BR>\n" );
document.write( "300=2L+2W<BR>\n" );
document.write( "300-2L=-2L+2L+2W<BR>\n" );
document.write( "300-2L=2W<BR>\n" );
document.write( "(300-2L)/2=2W/2<BR>\n" );
document.write( "300/2-2L/2=W<BR>\n" );
document.write( "150-L=W<BR>\n" );
document.write( "A=LW  We only want one variable, so substitute the value above in for W.<BR>\n" );
document.write( "A=L(150-L)<BR>\n" );
document.write( "A=150L-L^2<BR>\n" );
document.write( "A=-L^2+150L<BR>\n" );
document.write( "A=-(L^2-150L)<BR>\n" );
document.write( "A=-(L^2-150L+(150/2)^2)+(150/2)^2<BR>\n" );
document.write( "A=-(L^2-150L+75^2)+75^2<BR>\n" );
document.write( "A=-(L-75)^2+5625<BR>\n" );
document.write( "The vertex of a parabola represents the maximum or minimum of the parabola.<BR>\n" );
document.write( "The vertex form of a parabola is f(x)=a(x-h)^2+k where the vertex is (h,k).<BR>\n" );
document.write( "In our case the vertex is (75,5625)<BR>\n" );
document.write( "Our maximum L value we get from the h coordinate of our vertex=75 ft.  That's our maximum length.<BR>\n" );
document.write( "Our maximum W (width) value is 150-L=150-75=75 ft.<BR>\n" );
document.write( "Our maximum area we get from the k value of our vertex= 5625 ft.  </SPAN>\n" );
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