Perimeter of a rectangle is:

2l + 2w = P

However, we're given one side (length) is bordered by the river and the fence length is 800, so we have:

So we have l + 2w = 800

Rearranging in terms of l, we have:

l = 800 - 2w

The Area of a rectangle is:

A = lw

Plug in the value for l in the perimeter into this:

A = (800 - 2w)w

A = 800w - 2w^2

Take the first derivative:

A' = 800 - 4w

Now set this equal to 0 for maximum points:

4w = 800

Typing this equation into the search engine, we get:

w = 200

Now plug this into our perimeter equation:

l = 800 - 2(200)

l = 800 - 400

l = 400

The maximum area to be enclosed is;

A = lw

A = 400(200)

A =

**80,000 square feet**