Farmer Ed has 8500 meters of fencing and wants to enclose a rectangular plot that borders on a river. If farmer Ed does not fence the side along the river, what is the largest are that can be enclosed?

Width = 2x

Length = 8,500-2x

Let x and y be width and length of the plot to be fenced. Therefore,

Area (A) = xy m^2

If the side bordering the river is x, then

Circumference (C) = 8500 = x+2y = > x = 8500-2y

Substituting for w in the equation for A;

A = (8500-2y) y = 8500y - 2y^2

For maximum area, derivative of A with respect to y is 0. That is;

dA/dy = 0 = 8500 - 4y = > 4y = 8500 = > y = 8500/4 = 2125 m

And, x = 8500-2y = 8500 - 2*2125 = 4250 m

Therefore,

One side = 4,250 m and second side = 2,125 m.

Largest area, A = 4250*2125 = 9,031,250 m^2