document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1051181>Question 1051181</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me how to solve this problem.Thanks.\r<BR>\n" );
document.write( "\n" );
document.write( "Ramon wants to fence in a rectangular portion of his back yard against the back of his garage for a vegetable garden. He plans to use 68 feet of fence, and needs fence on only three sides. Find the maximum area he can enclose. (Hint: The lengths of the 3 fenced sides of the rectangle must add up to 68.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #666756 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=666756\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we know that<BR>\n" );
document.write( ":<BR>\n" );
document.write( "1) l + 2w = 68, where l is the length and w is the width of the rectangle<BR>\n" );
document.write( ":<BR>\n" );
document.write( "also<BR>\n" );
document.write( ":<BR>\n" );
document.write( "2) l * w = Area of the rectangle<BR>\n" );
document.write( ":<BR>\n" );
document.write( "solve equation 1) for l<BR>\n" );
document.write( ":<BR>\n" );
document.write( "l = 68 - 2w<BR>\n" );
document.write( ":<BR>\n" );
document.write( "substitute for l in equation 2)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "w * (68 - 2w) = Area <BR>\n" );
document.write( ":<BR>\n" );
document.write( "-2w^2 + 68w = Area<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The equation for the Area in terms of w is a parabola that opens downward, so<BR>\n" );
document.write( "we know that w is maximum at the vertex<BR>\n" );
document.write( ":<BR>\n" );
document.write( "To find w, we take the first derivative of the equation for Area, then set it <BR>\n" );
document.write( "equal to 0 and solve for w<BR>\n" );
document.write( ":<BR>\n" );
document.write( "-4w + 68 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "-4w = -68<BR>\n" );
document.write( ":<BR>\n" );
document.write( "w = 17<BR>\n" );
document.write( ":<BR>\n" );
document.write( "l = 68 -2(17) = 34<BR>\n" );
document.write( ":<BR>\n" );
document.write( "*****************************************<BR>\n" );
document.write( "Maximum Area is 34 * 17 = 578 square feet<BR>\n" );
document.write( "*****************************************<BR>\n" );
document.write( ":\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );