document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1033413>Question 1033413</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Stacy has 30 meters of fencing that she wishes to use to enclose a rectangular garden. If all of the fencing is used, what is the maximum area of the garden, in square meters, that can be enclosed?\r<BR>\n" );
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document.write( "A)48.75<BR>\n" );
document.write( "B)56.25<BR>\n" );
document.write( "C)60.50<BR>\n" );
document.write( "D)168.75 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #648031 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=648031\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The maximum area for a rectangle is when it is a square.  This can be proven a variety of ways, but I will use that.<BR>\n" );
document.write( "7.5 m on a side<BR>\n" );
document.write( "7.5^2=56.25 sq m.  B\r<BR>\n" );
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document.write( "Let x equal a side of a rectangle and y equal the other side<BR>\n" );
document.write( "P=2x+2y<BR>\n" );
document.write( "(P-2y)/2=x<BR>\n" );
document.write( "area ix xy=y(P-2y)/2=[Py-2y^2]/2<BR>\n" );
document.write( "The maximum of this quadratic (which has a vertex at highest point, because the y^2 coefficient is negative is at (1/2)(P-4y).<BR>\n" );
document.write( "Set that equal to 0, multiply by 2 and move terms, and 4y must equal P.<BR>\n" );
document.write( "y=(1/4)P, and that is a square.<BR>\n" );
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