Question 343917
For this rectangle,
{{{P=2W+L=240}}}
The {{{L}}} side is parallel to the river.
The area of this rectangle is,
{{{A=L*W}}}
From the perimeter equation,
{{{L=240-2W}}}
Substitute in the area equation,
{{{A=(240-2W)W}}}
{{{A=240W-2W^2}}}
Convert the area equation to vertex form, {{{y=a(x-h)^2+k}}}.
The function has a maximum at the vertex (h,k).
Complete the square to convert to vertex form.
{{{A=-2W^2+240W}}}
{{{A=-2(W^2-120W)}}}
{{{A=-2(W^2-120W+3600)+2(3600)}}}
{{{A=-2(W-60)^2+7200}}}
The maximum area of 7200 sq.m. occurs when W=60m.
{{{L=240-2(60)}}}
{{{L=240-120}}}
{{{L=120}}}m
The rectangular field if 60m x 120m.