document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=71238>Question 71238</A>: <I><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 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 #50968 by </B><A HREF=/tutors/aboutme.mpl?userid=galactus><B>galactus(183)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=galactus><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/cgi-bin/show-face.mpl?user=galactus><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=50968\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = the width and y = length of the patio. The perimeter of the patio can be represented by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=2x%2B2y=300 ALIGN=MIDDLE  ALT=\"P=2x%2B2y=300\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The area by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=xy ALIGN=MIDDLE  ALT=\"A=xy\"   DISABLED_style= \"max-width:90%; height:auto;\" >. See so far?.\r<BR>\n" );
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document.write( "Solve 2x+2y=300 for y and sub into the area formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28300-2x%29%2F2=150-x ALIGN=MIDDLE  ALT=\"y=%28300-2x%29%2F2=150-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, sub into area, xy:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28150-x%29=-x%5E2%2B150x ALIGN=MIDDLE  ALT=\"x%28150-x%29=-x%5E2%2B150x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You probably know the x-coordiante of the vertex is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F%282a%29 ALIGN=MIDDLE  ALT=\"-b%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a=-1 and b=150\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-150%2F%282%28-1%29%29=75 ALIGN=MIDDLE  ALT=\"-150%2F%282%28-1%29%29=75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, the width x, is 75. \r<BR>\n" );
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document.write( "Subbing gives us y=75 also.\r<BR>\n" );
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document.write( "Therefore, max area is achieved when the width is 75 and the length is 75.\r<BR>\n" );
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document.write( "It can be shown through calculus that the max area is achieved when the area is a square. Which you have. 75X75 square patio. </SPAN>\n" );
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