document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=310541>Question 310541</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the minimum perimeter possible for a rectangle with an area or 500cm squared </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #222090 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=222090\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Perimeter of a rectangle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=2%2A%28L%2BW%29 ALIGN=MIDDLE  ALT=\"P=2%2A%28L%2BW%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Area of a rectangle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=L%2AW=500 ALIGN=MIDDLE  ALT=\"A=L%2AW=500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=500%2FW ALIGN=MIDDLE  ALT=\"L=500%2FW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute this expression into the perimeter equation,<BR>\n" );
document.write( "P=2*(500/W+W)<BR>\n" );
document.write( "Now perimeter is a function only of W.<BR>\n" );
document.write( "To find the minimum, take the derivative wrt W and set it equal to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=1000%2FW%2B2W=1000W%5E%28-1%29%2B2W ALIGN=MIDDLE  ALT=\"P=1000%2FW%2B2W=1000W%5E%28-1%29%2B2W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dP%2FdW=-1000W%5E%28-2%29%2B2=2-1000%2FW%5E2=0 ALIGN=MIDDLE  ALT=\"dP%2FdW=-1000W%5E%28-2%29%2B2=2-1000%2FW%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000%2FW%5E2=2 ALIGN=MIDDLE  ALT=\"1000%2FW%5E2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5E2=500 ALIGN=MIDDLE  ALT=\"W%5E2=500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=sqrt%28500%29 ALIGN=MIDDLE  ALT=\"W=sqrt%28500%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2AW=500 ALIGN=MIDDLE  ALT=\"L%2AW=500\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=sqrt%28500%29 ALIGN=MIDDLE  ALT=\"L=sqrt%28500%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The shape that minimizes perimeter is a square of side <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28500%29 ALIGN=MIDDLE  ALT=\"sqrt%28500%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Pmin=4sqrt%28500%29 ALIGN=MIDDLE  ALT=\"Pmin=4sqrt%28500%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );