document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=343917>Question 343917</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular field is to be made along a river. if one side is to have the river as a natural boundary, what are the dimensions of the largest rectangular field that can be enclosed by using 240 meters of fence for the other 3 sides? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #246021 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=246021\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For this rectangle,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=2W%2BL=240 ALIGN=MIDDLE  ALT=\"P=2W%2BL=240\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" > side is parallel to the river.<BR>\n" );
document.write( "The area of this rectangle is,<BR>\n" );
document.write( "<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( "From the perimeter equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=240-2W ALIGN=MIDDLE  ALT=\"L=240-2W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute in the area equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28240-2W%29W ALIGN=MIDDLE  ALT=\"A=%28240-2W%29W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=240W-2W%5E2 ALIGN=MIDDLE  ALT=\"A=240W-2W%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Convert the area equation to vertex form, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The function has a maximum at the vertex (h,k).<BR>\n" );
document.write( "Complete the square to convert to vertex form.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-2W%5E2%2B240W ALIGN=MIDDLE  ALT=\"A=-2W%5E2%2B240W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-2%28W%5E2-120W%29 ALIGN=MIDDLE  ALT=\"A=-2%28W%5E2-120W%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=-2%28W%5E2-120W%2B3600%29%2B2%283600%29 ALIGN=MIDDLE  ALT=\"A=-2%28W%5E2-120W%2B3600%29%2B2%283600%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=-2%28W-60%29%5E2%2B7200 ALIGN=MIDDLE  ALT=\"A=-2%28W-60%29%5E2%2B7200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum area of 7200 sq.m. occurs when W=60m.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=240-2%2860%29 ALIGN=MIDDLE  ALT=\"L=240-2%2860%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=240-120 ALIGN=MIDDLE  ALT=\"L=240-120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=120 ALIGN=MIDDLE  ALT=\"L=120\"   DISABLED_style= \"max-width:90%; height:auto;\" >m<BR>\n" );
document.write( "The rectangular field if 60m x 120m.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );