document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=986771>Question 986771</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer wants to fence in a rectangular pen using the wall of a barn for one side of the pen and the 10 metres of fencing for the remaining three sides. What dimension will give him the maximum area for the pen? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #607562 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=607562\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> wall length =x<BR>\n" );
document.write( "long side length=x<BR>\n" );
document.write( "short side is (10-x)/2 for each.  The sum is 2x+5-(x/2)+5-(x/2)=10<BR>\n" );
document.write( "Area is x((1/2)(10-x)=<BR>\n" );
document.write( "(10x-x^2)/2=0<BR>\n" );
document.write( "by calculus the first derivative is 10-2x=0; x=5<BR>\n" );
document.write( "by quadratic,<BR>\n" );
document.write( "(10x-x^2)/2=0<BR>\n" );
document.write( "vertex of this is -b/2a=5/1=5<BR>\n" );
document.write( "The dimensions are 5m X 2.5m=12.5m^2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C20%2C-0.5x%5E2%2B5x%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C20%2C-0.5x%5E2%2B5x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );