The size of a square computer screen is measured by the length of its diagonal. How much bigger is the visible area of

[M7MBA]

The size of a square computer screen is measured by the length of its diagonal. How much bigger is the visible area of a square 24-inch screen than the area of a square 20-inch screen?

A. 80
B. 82
C. 84
D. 86
E. 88

Answer: E

Source: Manhattan GMAT

[Scott@TargetTestPrep]

The size of a square computer screen is measured by the length of its diagonal. How much bigger is the visible area of a square 24-inch screen than the area of a square 20-inch screen?

A. 80
B. 82
C. 84
D. 86
E. 88

Answer: E

Solution:

Recall that the area of a square is d^2/2 where d is the diagonal of the square. Therefore, a square 24-inch screen has an area of 24^2/2 = 576/2 = 288 square inches and a square 20-inch screen has an area of 20^2/2 = 400/2 = 200 square inches. We see that the area of the former is 288 - 200 = 88 square inches larger than that of the latter.

Alternate Solution:

Recall that the diagonal of a square cuts the square into two 45-45-90 triangles, each with side x and hypotenuse (diagonal) of x√2. Since the diagonal of the 24-inch screen is 24 inches, we have

x√2 = 24

x = 24/√2

Thus, the area of the 24-inch screen is (24/√2)^2 = 288 square inches.

Similarly, for the 20-inch screen, the diagonal is

x√2 = 20

x = 20/√2,

and the area of the entire screen is (20/√2)^2 = 200 square inches.

Thus, the difference in the two monitors’ areas is 288 - 200 = 88 square inches.

Answer: E