document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=825456>Question 825456</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I really appreciate if you could help me with following math problem. Thanks!! \r<BR>\n" );
document.write( "\n" );
document.write( "A farmer has 216 feet of fencing and wants to build two identical pens for his price-winning pigs.The pens will be arranged as shown. Determine the dimensions of a pen that will maximize its area. The solution is given, it would be 27' x 36'. <BR>\n" );
document.write( "[ | ] these two pens share 1 side, the middle one;  x is the width and y represents the length.\r<BR>\n" );
document.write( "\n" );
document.write( "I just can't figure out how to solve it. \r<BR>\n" );
document.write( "\n" );
document.write( "I reckon that the perimeter 216= 3x+ 2y and the area A= x times 2y. <BR>\n" );
document.write( "I figured out that in this case y= 108 - (3x/2). <BR>\n" );
document.write( "-> A= 2*(108- (3x/2)* x<BR>\n" );
document.write( "    = (216-3x)*x<BR>\n" );
document.write( "    = 3x^2-216x<BR>\n" );
document.write( "    = 3 (x^2 - 72x    )<BR>\n" );
document.write( "    = 3 (x^2 -72x + 1296)  -1296<BR>\n" );
document.write( "    = 3 (x-36)^2           -1296 (which I though is the product maximum)\r<BR>\n" );
document.write( "\n" );
document.write( "36 is one factor of 1296 and as I know one of the solutions. Therefore 27 should be the other solution but it cannot multiply with 36 to a product of 1296. That is why I'm superconfused. Please help me as quickly as possible. Thanks in advanced. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497309 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=497309\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The picture or diagram is not shown to us, but your fencing formula which I would not really call as \"perimeter\", is correct, indicating that x is one of the lengths of the divider as well as one of the dimensions of the whole rectangular form.  y is the other dimension of the whole rectangular form.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Your mistake only appears to be your area formulation.  This should be, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28A=xy%29 ALIGN=MIDDLE  ALT=\"highlight_green%28A=xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >;\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "From this, you may find no further trouble nor confusion. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );