(A) 120

(B) 106.5

(C) 93.5

(D) 87.5

(E) 80

Let's say the width of the shed is W and the length is L. Then we know that

2W + 2L = 40, or W + L = 20 and

W

^{2}+ L^{2}= 15^{2}= 225.If we square both sides of the first equation, we get

(W+L)

^{2}= 400W

^{2}+ L^{2}+ 2WL = 400.Since we know that W

^{2}+ L^{2}= 225, we can simplify the equation to225 + 2WL = 400

2WL = 175

WL = 87.5

The quantity WL is the area of the shed, since the area of a rectangle is width times length. So the correct answer is D.