document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=758375>Question 758375</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ok. I need to find the optimum perimeter for a rectangle with the area of 242cm squared. My teacher didn't even teach us he just gave it to us and said do it. I am in grade 8. I would appreciate if you could really expand on this so I can understand. THANKS :D </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #461443 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=461443\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I need to find the optimum perimeter for a rectangle with the area of 242cm squared.<BR>\n" );
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document.write( "You can find the minimum perimeter, not sure what optiumum would be.<BR>\n" );
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document.write( "Pick a perimeter and find the max area: P = 100<BR>\n" );
document.write( "P = 2L + 2W = 100<BR>\n" );
document.write( "L + W = 50<BR>\n" );
document.write( "L = 50 - W<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "Area = L*W = W*(50 - W)<BR>\n" );
document.write( "Area = 50W - W^2<BR>\n" );
document.write( "W^2 - 50W + Area = 0<BR>\n" );
document.write( "It's a quadratic in W<BR>\n" );
document.write( "Ther vertex is on the Axis of Symmetry which is<BR>\n" );
document.write( "W = -b/2a<BR>\n" );
document.write( "----<BR>\n" );
document.write( "W = 50/2 = 25<BR>\n" );
document.write( "L = 25<BR>\n" );
document.write( "---> Max area of a rectangle of given perimeter is a square.<BR>\n" );
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document.write( "For Area = 242<BR>\n" );
document.write( "L = W = sqrt(242)<BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"11%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm<BR>\n" );
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