document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1097035>Question 1097035</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Marlon wants to fence a rectangular area that has one side bordered by an irrigation. If he has 80 m of fencing materials, what are the dimensions and the maximum area he can enclose? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #711536 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=711536\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the length along be irrigation side by Y and the width be X.<BR>\n" );
document.write( "The fence would then have a perimeter of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=2X%2BY=80 ALIGN=MIDDLE  ALT=\"P=2X%2BY=80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The area enclosed would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=XY ALIGN=MIDDLE  ALT=\"A=XY\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the perimeter equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=80-2X ALIGN=MIDDLE  ALT=\"Y=80-2X\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting into the area equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=X%2880-2X%29=-2X%5E2%2B80X ALIGN=MIDDLE  ALT=\"A=X%2880-2X%29=-2X%5E2%2B80X\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To find the maximum area, convert to vertex form,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28X%29=-2%28X%5E2-40X%29 ALIGN=MIDDLE  ALT=\"A%28X%29=-2%28X%5E2-40X%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%28X%29=-2%28X%5E2-40X%2B400%29%2B800 ALIGN=MIDDLE  ALT=\"A%28X%29=-2%28X%5E2-40X%2B400%29%2B800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28X%29=-2%28X-20%29%5E2%2B800 ALIGN=MIDDLE  ALT=\"A%28X%29=-2%28X-20%29%5E2%2B800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the maximum area of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=800 ALIGN=MIDDLE  ALT=\"800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2 ALIGN=MIDDLE  ALT=\"m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > occurs when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=20 ALIGN=MIDDLE  ALT=\"X=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=80-2%2820%29 ALIGN=MIDDLE  ALT=\"Y=80-2%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=80-40 ALIGN=MIDDLE  ALT=\"Y=80-40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=40 ALIGN=MIDDLE  ALT=\"Y=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );