document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=463628>Question 463628</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am stuck on this problem, any help would be greatly appreciated. \r<BR>\n" );
document.write( "\n" );
document.write( "Given a rectangle with a fixed perimeter of 372 feet, what dimensions would yield the maximum area? What is 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 #317660 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=317660\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am stuck on this problem, any help would be greatly appreciated. <BR>\n" );
document.write( "Given a rectangle with a fixed perimeter of 372 feet, what dimensions would yield the maximum area? What is the maximum area<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Standard form for parabola: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.<BR>\n" );
document.write( "let x=length of rectangle<BR>\n" );
document.write( "let y= width of rectangle<BR>\n" );
document.write( "2x+2y=372<BR>\n" );
document.write( "x+y=186<BR>\n" );
document.write( "y=186-x<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Area=x*y=x(186-x)=186x-x^2<BR>\n" );
document.write( "Area=-x^2+186x<BR>\n" );
document.write( "completing the square<BR>\n" );
document.write( "-(x^2-186x+(186/2)^2)+(186/2)^2<BR>\n" );
document.write( "-(x-93)^2+(93)^2=-(x-93)^2+8649<BR>\n" );
document.write( "This equation is a parabola with vertex at (93,8649)<BR>\n" );
document.write( "Dimensions:<BR>\n" );
document.write( "x=93 ft<BR>\n" );
document.write( "y=186-x=93 ft<BR>\n" );
document.write( "maximum area=8649 sq ft </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );