Solution:
For a rectangular play area, the perimeter (P) is given by the formula P = 2l + 2w, where l is the length and w is the width.

In this case, Corinda has 400 feet of fencing, so 2l + 2w = 400.
Now, solve for l: l = 400 / 4 = 100.

So, the length (l) and width (w) of the rectangular play area should be 100 feet each, forming a square, which maximizes the enclosed area.