document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=628179>Question 628179</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a rectangle with length L and width W has a perimeter of 4 cm, what are the definitions of the rectangle with the largest area and what is that area? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #395430 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=395430\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula for perimeter is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+2L+%2B+2W+ ALIGN=MIDDLE  ALT=\"+P+=+2L+%2B+2W+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+4+ ALIGN=MIDDLE  ALT=\"+P+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4+=+2L+%2B+2W+ ALIGN=MIDDLE  ALT=\"+4+=+2L+%2B+2W+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+=+L+%2B+W+ ALIGN=MIDDLE  ALT=\"+2+=+L+%2B+W+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+W+=+2+-+L+ ALIGN=MIDDLE  ALT=\"+W+=+2+-+L+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------<BR>\n" );
document.write( "The formula for area is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+W%2AL+ ALIGN=MIDDLE  ALT=\"+A+=+W%2AL+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "By substitution:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+%28+2+-+L+%29%2AL+ ALIGN=MIDDLE  ALT=\"+A+=+%28+2+-+L+%29%2AL+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+-L%5E2+%2B+2L+ ALIGN=MIDDLE  ALT=\"+A+=+-L%5E2+%2B+2L+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a parabola with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > plotted on the<BR>\n" );
document.write( "vertical axis and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+ ALIGN=MIDDLE  ALT=\"+L+\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the horizontal.<BR>\n" );
document.write( "The minus sign in front of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L%5E2+ ALIGN=MIDDLE  ALT=\"+L%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > means<BR>\n" );
document.write( "the parabola has a maximum, not a minimum.<BR>\n" );
document.write( "------------------------------------<BR>\n" );
document.write( "If the equation has the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28L%29+=+a%2AL%5E2+%2B+b%2AL+%2B+c+ ALIGN=MIDDLE  ALT=\"+f%28L%29+=+a%2AL%5E2+%2B+b%2AL+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "then the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+ ALIGN=MIDDLE  ALT=\"+L+\"   DISABLED_style= \"max-width:90%; height:auto;\" > coordinate of the maximum is at<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-1+ ALIGN=MIDDLE  ALT=\"+a+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+2+ ALIGN=MIDDLE  ALT=\"+b+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L%5Bmax%5D+=+-2%2F%282%2A%28-1%29%29+ ALIGN=MIDDLE  ALT=\"+L%5Bmax%5D+=+-2%2F%282%2A%28-1%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L%5Bmax%5D+=+1+ ALIGN=MIDDLE  ALT=\"+L%5Bmax%5D+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the max is at ( 1,A ) where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+ ALIGN=MIDDLE  ALT=\"+A+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+-1%5E2+%2B+2%2A1+ ALIGN=MIDDLE  ALT=\"+A+=+-1%5E2+%2B+2%2A1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+-1+%2B+2+ ALIGN=MIDDLE  ALT=\"+A+=+-1+%2B+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+1+ ALIGN=MIDDLE  ALT=\"+A+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "The maximum area is 1 cm2<BR>\n" );
document.write( "and, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L=1+ ALIGN=MIDDLE  ALT=\"+L=1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+W+=+2+-+L+ ALIGN=MIDDLE  ALT=\"+W+=+2+-+L+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+W+=+2+-+1+ ALIGN=MIDDLE  ALT=\"+W+=+2+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+W+=+1+ ALIGN=MIDDLE  ALT=\"+W+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the maximum area is when the rectangle is a square<BR>\n" );
document.write( "with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L=W=1+ ALIGN=MIDDLE  ALT=\"+L=W=1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );