document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=724271>Question 724271</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help setting a word problem up. If someone could please show me the equations I need to solve this:\r<BR>\n" );
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document.write( "a farmer is fencing a rectangular area for cattle using a straight portion of the river as one side of the rectangle. There is no fencing along the river. If the farmer has 1200 feet of fence, find the dimensions for the rectangular area that gives a maximum area for the cattle.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #443688 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=443688\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a farmer is fencing a rectangular area for cattle using a straight portion of the river as one side of the rectangle. There is no fencing along the river. If the farmer has 1200 feet of fence, find the dimensions for the rectangular area that gives a maximum area for the cattle.<BR>\n" );
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document.write( "let x=width (perpendicular to river)<BR>\n" );
document.write( "let y=length (parallel to river)<BR>\n" );
document.write( "2x+y=1200<BR>\n" );
document.write( "y=1200-2x<BR>\n" );
document.write( "area=length*width<BR>\n" );
document.write( "xy=x(1200-2x)=1200x-2x^2<BR>\n" );
document.write( "Area=-2x^2+1200x<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "Area=-2(x^2-600x+300^2)+2(300^2)<BR>\n" );
document.write( "Area=-2(x-300)^2+180000<BR>\n" );
document.write( "This is an equation of the standard form for a parabola that opens downward: y=-A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex from which the x-value which gives the maximum area and the maximum area itself is obtained.<BR>\n" );
document.write( "x=300<BR>\n" );
document.write( "y=1200-2x=600<BR>\n" );
document.write( "dimensions for the rectangular area that gives a maximum area for the cattle:<BR>\n" );
document.write( "width=300 ft<BR>\n" );
document.write( "length=600 ft<BR>\n" );
document.write( "maximum area=180,000 sq ft<BR>\n" );
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