document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177927>Question 177927</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Smith's have 160 meters of fencing available to build a rectangular garden. One side of the garden touches a side of the house and doesn't need any bordering. Algebraically find the dimensions that will give 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 #132945 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=132945\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One side of the rectangle is taken up by the house. <BR>\n" );
document.write( "That leaves 3 sides taken up by fencing. <BR>\n" );
document.write( "Let's call that side W for width and the other two sides will be L to use up the fencing.<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L%2BW=160 ALIGN=MIDDLE  ALT=\"2L%2BW=160\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The area of the rectangle will be<BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=L%2AW ALIGN=MIDDLE  ALT=\"A=L%2AW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use eq. 1 and make the area a function of only one variable.<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L%2BW=160 ALIGN=MIDDLE  ALT=\"2L%2BW=160\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=160-2L ALIGN=MIDDLE  ALT=\"W=160-2L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=L%2AW ALIGN=MIDDLE  ALT=\"A=L%2AW\"   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%2A%28160-2L%29 ALIGN=MIDDLE  ALT=\"A=L%2A%28160-2L%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=-2L%2A2%2B160L ALIGN=MIDDLE  ALT=\"A=-2L%2A2%2B160L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can differentiate with respect to L and set the derivative equal to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2FdL=-4L%2B160=0 ALIGN=MIDDLE  ALT=\"dA%2FdL=-4L%2B160=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=40 ALIGN=MIDDLE  ALT=\"L=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's plot the graph of area as a function of length to make sure the area is maximum at this point,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-20%2C+080%2C+-100%2C+4000%2C+-2x%5E2%2B160x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-20%2C+080%2C+-100%2C+4000%2C+-2x%5E2%2B160x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From eq. 1, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=160-2L ALIGN=MIDDLE  ALT=\"W=160-2L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=160-2%2840%29 ALIGN=MIDDLE  ALT=\"W=160-2%2840%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=80 ALIGN=MIDDLE  ALT=\"W=80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The area is then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=L%2AW=40%2A80=1250 ALIGN=MIDDLE  ALT=\"A=L%2AW=40%2A80=1250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Width of 80 m, length of 40 m, yields a garden of 3200 sq. meters. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );