Monday, May 23, 2011

(Q 358) GMAT / GRE Word Problem

A rectangular shed has a perimeter of 40 meters and a diagonal length of 15 meters. What is the area of the shed in square meters?

(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
W2 + L2 = 152 = 225.

If we square both sides of the first equation, we get

(W+L)2 = 400
W2 + L2 + 2WL = 400.

Since we know that W2 + L2 = 225, we can simplify the equation to

225 + 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.