document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62777>Question 62777</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could someone please help me with this. I just don't get algebra, but i'm getting better.<BR>\n" );
document.write( "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.<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 #43623 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=43623\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2*length+2*width=300<BR>\n" );
document.write( "Divide thru by 2 to get:<BR>\n" );
document.write( "length+width = 150<BR>\n" );
document.write( "Solve for width:<BR>\n" );
document.write( "width=150-length<BR>\n" );
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document.write( "Let the length be \"x\".<BR>\n" );
document.write( "Then the width = \"150-x\"<BR>\n" );
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document.write( "Area=(length)(width)<BR>\n" );
document.write( "Area=x(150-x)<BR>\n" );
document.write( "Area=-x^2+150x<BR>\n" );
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document.write( "This is a quadratic with a=-1 and b=150<BR>\n" );
document.write( "Maximum area occurs when x=-b/2a<BR>\n" );
document.write( "x=-150/(-2)=75<BR>\n" );
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document.write( "Dimensions are<BR>\n" );
document.write( "width = 75 ft.<BR>\n" );
document.write( "length = 150-75=75 ft.<BR>\n" );
document.write( "The maximum area is 75^2=5625 sq ft.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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