document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=437678>Question 437678</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using 36 feet of rope, enclose a rectangle with the largest possible area. Enclose a rectangle with the smallest possible area. In both cases use dimensions that are whole feet.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #302775 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=302775\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The largest possible area occurs when the figure is a square (it is possible to prove this using the vertex of a parabola, or by calculus, or by AM-GM inequality). If it is a square, the side length would be 9 ft, and the area is 81 ft.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The smallest possible area is about zero. This occurs when the length approaches zero and the width approaches 18. In rigorous terms, if L, 18-L are the length and width, then\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \lim_{L\to\0} L(18-L) = \lim_{L\to\0} (-L^2 + 18L) = 0\"> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );