document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150427>Question 1150427</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question 9: A rancher has 600 feet of fencing to put around a rectangular field and then subdivide the field into 3 identical smaller rectangular plots by placing two fences parallel to one of the field's shorter sides. Find the dimensions that maximize the enclosed area. Write your answers as fractions reduced to lowest terms. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #771804 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=771804\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+ ALIGN=MIDDLE  ALT=\"+w+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the width of the rectangle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4w+ ALIGN=MIDDLE  ALT=\"+4w+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the total of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+ ALIGN=MIDDLE  ALT=\"+w+\"   DISABLED_style= \"max-width:90%; height:auto;\" > lengths of fence<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+600+-+4w+%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+%28+600+-+4w+%29+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the length of the rectangle<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+ ALIGN=MIDDLE  ALT=\"+A+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the total area of the rectangle<BR>\n" );
document.write( "----------------------------------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+4w%2A%28+%28+600+-+4w+%29+%2F+2+%29+ ALIGN=MIDDLE  ALT=\"+A+=+4w%2A%28+%28+600+-+4w+%29+%2F+2+%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+=+2w%2A%28+600+-+4w+%29+ ALIGN=MIDDLE  ALT=\"+A+=+2w%2A%28+600+-+4w+%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+=+-8w%5E2+%2B+1200w ALIGN=MIDDLE  ALT=\"+A+=+-8w%5E2+%2B+1200w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a parabola with a maximum peak<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w%5Bpk%5D+=+-1200%2F%282%2A%28-8%29%29+ ALIGN=MIDDLE  ALT=\"+w%5Bpk%5D+=+-1200%2F%282%2A%28-8%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=+w%5Bpk%5D+=+75+ ALIGN=MIDDLE  ALT=\"+w%5Bpk%5D+=+75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plug this result back into equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+-8w%5E2+%2B+1200w ALIGN=MIDDLE  ALT=\"+A+=+-8w%5E2+%2B+1200w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bmax%5D+=+-8%2A75%5E2+%2B+1200%2A75 ALIGN=MIDDLE  ALT=\"+A%5Bmax%5D+=+-8%2A75%5E2+%2B+1200%2A75\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( formula for vertex of parabola )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bmax%5D+=+-45000+%2B+90000+ ALIGN=MIDDLE  ALT=\"+A%5Bmax%5D+=+-45000+%2B+90000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bmax%5D+=+45000+ ALIGN=MIDDLE  ALT=\"+A%5Bmax%5D+=+45000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+45000%2Fw%5Bpk%5D+=+45000%2F75+ ALIGN=MIDDLE  ALT=\"+45000%2Fw%5Bpk%5D+=+45000%2F75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+45000%2Fw%5Bpk%5D+=+600+ ALIGN=MIDDLE  ALT=\"+45000%2Fw%5Bpk%5D+=+600+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------------------------<BR>\n" );
document.write( "The dimensions that maximize area are:<BR>\n" );
document.write( "75' x 600'<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-20%2C+200%2C+-5000%2C+50000%2C+-8x%5E2+%2B+1200x+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-20%2C+200%2C+-5000%2C+50000%2C+-8x%5E2+%2B+1200x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );