It is given that length exceeds width by 2 feet. And if each of the dimensions is increased by 2 feet, the area will increase by 48 square feet.

Let the initial width be W. The length is W + 2

The area now is width*length = W*(W + 2).

When the dimensions are increased by 2 feet, the width becomes W + 2 and the length becomes W + 2 + 2 = W + 4

The area is (W + 2)*(W + 4)

We know that (W + 2)*(W + 4) - W*(W + 2) = 48

=> W^2 + 6W + 8 - W^2 - 2W = 48

=> 4W + 8 = 48

=> 4W = 40

=> W = 10

Length = width + 2 = 12

**The required dimensions are width = 10 feet and length = 12 feet.**