document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1089216>Question 1089216</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man has 30 feet of fence for a rectangular garden. What is the area of the largest garden he can build with whole-number dimensions?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #703554 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=703554\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let l be length and w be width<BR>\n" );
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document.write( "1) Area(A) of rectangle = l * w<BR>\n" );
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document.write( "2) 2l + 2w = 30 feet(perimeter of rectangular garden)<BR>\n" );
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document.write( "solve equation 2 for l<BR>\n" );
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document.write( "l + w = 15<BR>\n" );
document.write( "l = 15 - w<BR>\n" );
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document.write( "now substitute for l in expression for Area<BR>\n" );
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document.write( "(15-w) * w<BR>\n" );
document.write( "15w -w^2<BR>\n" );
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document.write( "this is the equation of a parabola that curves downward, therefore we could take the first derivative to find the coordinates of the vertex<BR>\n" );
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document.write( "the expression in standard form is<BR>\n" );
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document.write( "-w^2 +15w<BR>\n" );
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document.write( "the first derivative is -2w + 15<BR>\n" );
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document.write( "-2w +15 = 0<BR>\n" );
document.write( "-2w = -15<BR>\n" );
document.write( "w = 7.5 feet<BR>\n" );
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document.write( "we could use the equation for x coordinate(w in this case) of the vertex <BR>\n" );
document.write( "w = -b / 2a = -15 / (-2 * 1) = 7.5<BR>\n" );
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document.write( "the max area is 8 * 7 = 56 feet<BR>\n" );
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