document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=310895>Question 310895</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you find the dimensions of a rectangle with the smallest perimeter and an area of 120000 inches? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #222429 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=222429\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The area of a rectangle is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=L%2AW=120000 ALIGN=MIDDLE  ALT=\"A=L%2AW=120000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=120000%2FW ALIGN=MIDDLE  ALT=\"L=120000%2FW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The perimeter of a rectangle is,<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( "Substituting,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=2%2A%28120000%2FW%2BW%29 ALIGN=MIDDLE  ALT=\"P=2%2A%28120000%2FW%2BW%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now P is a function of W only.<BR>\n" );
document.write( "To minimize P, find 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=dP%2FdW=2%2A%28-120000%2FW%5E2%2B1%29=0 ALIGN=MIDDLE  ALT=\"dP%2FdW=2%2A%28-120000%2FW%5E2%2B1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120000%2FW%5E2=1 ALIGN=MIDDLE  ALT=\"120000%2FW%5E2=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%5E2=120000 ALIGN=MIDDLE  ALT=\"W%5E2=120000\"   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%28120000%29 ALIGN=MIDDLE  ALT=\"W=sqrt%28120000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the area equation above,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=120000%2FW=120000%2Fsqrt%28120000%29=sqrt%28120000%29 ALIGN=MIDDLE  ALT=\"L=120000%2FW=120000%2Fsqrt%28120000%29=sqrt%28120000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The rectangle with the smallest perimeter and area of 120000 sq. in. is a square with sides of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28120000%29 ALIGN=MIDDLE  ALT=\"sqrt%28120000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );