document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=958223>Question 958223</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the dimensions that produce the maximum floor area for a one-story house that is rectangular in shape and has a perimeter of 151ft<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #585633 by </B><A HREF=/tutors/aboutme.mpl?userid=LinnW><B>LinnW(1048)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=LinnW><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=LinnW><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=585633\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> perimeter  = 2 * length + 2 * width<BR>\n" );
document.write( "set L = length , W = width<BR>\n" );
document.write( "perimeter = 2L + 2W<BR>\n" );
document.write( "since perimeter is to be 151<BR>\n" );
document.write( "151 = 2L + 2W<BR>\n" );
document.write( "Solving for L,<BR>\n" );
document.write( "151 - 2W = 2L<BR>\n" );
document.write( "dividing each side by2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28151+-+2W%29%2F2+=+2L%2F2 ALIGN=MIDDLE  ALT=\"%28151+-+2W%29%2F2+=+2L%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28151+-+2W%29%2F2+=+L ALIGN=MIDDLE  ALT=\"%28151+-+2W%29%2F2+=+L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since area = L*W<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+area+=+%28%28151+-+2W%29%2F2%29+%2A+W+ ALIGN=MIDDLE  ALT=\"+area+=+%28%28151+-+2W%29%2F2%29+%2A+W+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+area+=+%28151W+-+2W%5E2%29%2F2+ ALIGN=MIDDLE  ALT=\"+area+=+%28151W+-+2W%5E2%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiplying each side by 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+%2A+area+=+%28151W+-+2W%5E2%29+ ALIGN=MIDDLE  ALT=\"+2+%2A+area+=+%28151W+-+2W%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "set y = 2*area<BR>\n" );
document.write( "If we maximize the value of y in the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28151W+-+2W%5E2%29+ ALIGN=MIDDLE  ALT=\"+y+=+%28151W+-+2W%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we will can determine the best dimensions for L and W<BR>\n" );
document.write( "rewriting<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-2W%5E2+%2B+151W+ ALIGN=MIDDLE  ALT=\"+y+=+-2W%5E2+%2B+151W+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the coordinate values a = -2 and b = 151<BR>\n" );
document.write( "the value of W where y is maximum occurs when -b/2a is the value of W.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F2a+=+-%28151%2F2%28-2%29%29 ALIGN=MIDDLE  ALT=\"-b%2F2a+=+-%28151%2F2%28-2%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=-b%2F2a+=+151%2F4 ALIGN=MIDDLE  ALT=\"-b%2F2a+=+151%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "area will be maximum when W = 151/4<BR>\n" );
document.write( "We previously determined <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+=+%28151-2W%29%2F2+ ALIGN=MIDDLE  ALT=\"+L+=+%28151-2W%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > so substituting we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+=+%28151-2%28151%2F4%29%29%2F2+ ALIGN=MIDDLE  ALT=\"+L+=+%28151-2%28151%2F4%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+=+%28151-%28151%2F2%29%29%2F2+ ALIGN=MIDDLE  ALT=\"+L+=+%28151-%28151%2F2%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+=+%28151%2F2%29%2F2+ ALIGN=MIDDLE  ALT=\"+L+=+%28151%2F2%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+=+151%2F4+ ALIGN=MIDDLE  ALT=\"+L+=+151%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the maximum area will occur when W = 151/4 and L = 151/4 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );