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