document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=71236>Question 71236</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 formula 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" );
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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 #50952 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=50952\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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 are-1a 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. <BR>\n" );
document.write( "Show clearly the algebraic steps which prove your dimensions are the maximum area which can be obtained. Use the vertex formula to find the maximum area. <BR>\n" );
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document.write( "Perimeter = 2(l+w)=300 ft<BR>\n" );
document.write( "l+w=150<BR>\n" );
document.write( "l=150-w<BR>\n" );
document.write( "Area = lw<BR>\n" );
document.write( "Area = (150-w)w<BR>\n" );
document.write( "A = -w^2 + 150w<BR>\n" );
document.write( "This is a quadratic with a= -1; b= 150<BR>\n" );
document.write( "The vertex is at w = -b/2a = -150/-2 = 75 ft. (this is the width of the rectangle)<BR>\n" );
document.write( "l = 150-w = 150 - 75 = 75 ft (this is the length of the rectangle)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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