document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=42205>Question 42205</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321279085/algebrahomeworkh>college algebra gary rockswold</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Could someone please help me with this Thanks!!!!!!!\r<BR>\n" );
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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. <BR>\n" );
document.write( "Show clearly the algebraic steps which prove your dimensions are the maximum area which can be obtained. <BR>\n" );
document.write( "Answer: <BR>\n" );
document.write( "Show work in this space.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27365 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27365\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let length = L ft, width = W ft.<BR>\n" );
document.write( "Then perimeter = 300 = 2(L + W)<BR>\n" );
document.write( "or L + W =150 _____(1)\r<BR>\n" );
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document.write( "Now, area is given by<BR>\n" );
document.write( "A = W x L <BR>\n" );
document.write( "= (150 - L) x L <BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150L+-+L%5E2 ALIGN=MIDDLE  ALT=\"150L+-+L%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%5E2+-+%28L%5E2+-+2%2AL%2A75+%2B+75%5E2%29 ALIGN=MIDDLE  ALT=\"75%5E2+-+%28L%5E2+-+2%2AL%2A75+%2B+75%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+75%5E2+-+%28L+-+75%29%5E2 ALIGN=MIDDLE  ALT=\"A+=+75%5E2+-+%28L+-+75%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >________(2)\r<BR>\n" );
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document.write( "For 'A' to be maximum, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L+-+75%29%5E2 ALIGN=MIDDLE  ALT=\"%28L+-+75%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > has to be minimum.<BR>\n" );
document.write( "But it is a real square and hence cannot be negative.<BR>\n" );
document.write( "So its minimum value is zero. <BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L+-+75%29%5E2+=+0 ALIGN=MIDDLE  ALT=\"%28L+-+75%29%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or L = 75\r<BR>\n" );
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document.write( "We have obtained L = 75. Putting this value in (1) we find W = 75.\r<BR>\n" );
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document.write( "Putting L = 75 in (2) we will get the maximum value of 'A'.<BR>\n" );
document.write( "A<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28max%29+=+75%5E2+-+%2875+-+75%29%5E2+=+75%5E2 ALIGN=MIDDLE  ALT=\"%28max%29+=+75%5E2+-+%2875+-+75%29%5E2+=+75%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5625\r<BR>\n" );
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document.write( "So the maximum area of the patio is 5625 sq ft and its dimensions are 75 ft x 75 ft. In other words for maximum area, the patio is a square with side 75 ft. </SPAN>\n" );
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