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 #43625 by </B><A HREF=/tutors/aboutme.mpl?userid=jai_kos><B>jai_kos(139)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jai_kos><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=43625\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let L be the length<BR>\n" );
document.write( "Let W be the width<BR>\n" );
document.write( "We know the perimeter is:<BR>\n" );
document.write( "2(L + W) = 300<BR>\n" );
document.write( "Solving for L:<BR>\n" );
document.write( "L + W = 150<BR>\n" );
document.write( "L = 150 - W\r<BR>\n" );
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document.write( "Now write a formula for the area:<BR>\n" );
document.write( "Area = L * W<BR>\n" );
document.write( "Area = (150 - W) * W<BR>\n" );
document.write( "Area = -W² + 150W\r<BR>\n" );
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document.write( "You can see this is the formula for a parabola. I'll simplify things by expressing it in terms of x:<BR>\n" );
document.write( "f(x) = -x² + 150x\r<BR>\n" );
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document.write( "But it isn't in vertex form:<BR>\n" );
document.write( "f(x) = a(x - h) + k\r<BR>\n" );
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document.write( "To get it in that form, first pull out the -1 to get x²:<BR>\n" );
document.write( "f(x) = -1(x² - 150x)\r<BR>\n" );
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document.write( "Now take the coefficient on the x term (-150), take half of it (-75) and square it (5625). Add and subtract this:<BR>\n" );
document.write( "f(x) = -1(x² - 150x + 5625 - 5625)<BR>\n" );
document.write( "Now you can write this as a square:<BR>\n" );
document.write( "f(x) = -1[ (x - 75)(x - 75) - 5625)<BR>\n" );
document.write( "Simplify:<BR>\n" );
document.write( "f(x) = -1(x - 75)² + 5625\r<BR>\n" );
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document.write( "You have a downward facing parabola, with a maximum vertex at the point (h, k) or (75, 5625)\r<BR>\n" );
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document.write( "So the maximum is when the width is 75. When you solve for length you get that the length is also 75. So the maximum area for the patio is a square with sides of length 75 feet. The total area will be 5,625 sq. feet, a maximum.  </SPAN>\n" );
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