Answer
The width of the rectangle is 100 yards; the length is 400 yards.
Work Step by Step
$$x(2x+200)=40000$$
$$2x^2+200x=40000$$
$$2x^2+200x-40000=0$$
$$x^2+100x-20000=0$$
$$(x+200)(x-100)=0$$
$$x=-200,100$$
Length cannot be negative; x=100
The width of the rectangle is 100 yards; the length is 400 yards.