If one side (width) of a rectangle is x ft, then the opposite is also x and adjacent sides (length) have length of (2000 - 2x)/2 = 1000-x (as at your picture).

So a) the area A(x) = x*(1000-x) (square fts).

b) A(x) = -x^2 + 1000x = -(x-500)^2 +500^2 <= 500^2. Therefore A(x) has a maximum at x=500(ft). Width=500ft and length=1000-500=500ft.