document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183771>Question 1183771</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular field will be fenced on all four sides.  There will also be a line of fence across the field, parallel to the shorter side.  If 900m of fencing are available, what dimensions of the field will produce the maximum area?  What is the maximum area?<BR>\n" );
document.write( "Write a function f(x) to find the area, if x is the length of the fence going across the field.<BR>\n" );
document.write( "What is the maximum area that can be enclosed by using all of the fencing material and the fence lengths? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814231 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=814231\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Draw this.<BR>\n" );
document.write( "Long side is x and sum is 2x<BR>\n" );
document.write( "Short side is y and sum is 3y, since there is an extra fence<BR>\n" );
document.write( "We know that each short side fences is  (1/3) (900-2x) or 300-(2/3)x<BR>\n" );
document.write( "the area is x*(300-(2/3)x)=300x-(2/3)x^2. This is f(x)\r<BR>\n" );
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document.write( "and that has to be maximized<BR>\n" );
document.write( "the vertex for this negative quadratic is x=-b/2a or -300/(-4/3)=225 m<BR>\n" );
document.write( "so the dimensions are 225 m x 150 m, and the area is 33750 m^2.<BR>\n" );
document.write( "The length is 225 m and each width is 150 m  </SPAN>\n" );
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