document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=66575>Question 66575</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0132191415/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Amanda has 400 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). She wants to maximize the area of her patio (area of a rectangle is length times width). What should the dimensions of the patio be, and show how the maximum area of the patio is calculated from the algebraic equation.  Use the vertex form to find the maximum area. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #47214 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=47214\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Amanda has 400 feet of lumber to frame a<BR>\n" );
document.write( "rectangular patio (the perimeter of a rectangle is 2<BR>\n" );
document.write( "times length plus 2 times width). She wants to<BR>\n" );
document.write( "maximize the area of her patio (area of a rectangle is<BR>\n" );
document.write( "length times width). What should the dimensions of the<BR>\n" );
document.write( "patio be, and show how the maximum area of the patio<BR>\n" );
document.write( "is calculated from the algebraic equation.<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "IF L AND B ARE DIMENSIONS WE HAVE<BR>\n" );
document.write( "PERIMETER=2(L+B)=400.....OR.....L+B=200..OR......B=200-L.................I<BR>\n" );
document.write( "AREA=A<BR>\n" );
document.write( "=LB=L(200-L)=200L-L^2=-{L^2-200L}=-{(L^2)-2(L)(100)+100^2-100^2}<BR>\n" );
document.write( "A=10000-(L-100)^2<BR>\n" );
document.write( "(L-100)^2 BEING PERFECT SQUARE,ITS MINIMUM VALUE IS<BR>\n" );
document.write( "ZERO.<BR>\n" );
document.write( "HENCE AREA IS MAXIMUM WHEN L-100 IS ZERO,OR WHEN L=100<BR>\n" );
document.write( "AND THEN THE MAXIMUM AREA WOULD BE<BR>\n" );
document.write( "A-MAX.=10000-0=10000<BR>\n" );
document.write( "DIMENSIONS ARE 100*100 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );