The size of a square computer screen is measured by the leng

Question

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

Bunuel · Answer

We need to find the difference between the areas.

The area of a square is  \frac{diagonal^2}{2} .

Therefore the difference is 24^2/2 - 20^2/2 = 88.

Hope it's clear.

jlgdr · Answer

First screen s \sqrt{2} = 24
So 's' (standing for side of the square) =  \frac{24}{\sqrt{2}}

Second Screen s \sqrt{2} = 20
So 's' =  \frac{20}{\sqrt{2}}

So difference in their areas will be:

\frac{24^2}{2}-\frac{20^2}{2} = \frac{(24+20)(24-20)}{2} = 88

ScottTargetTestPrep · Answer

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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The size of a square computer screen is measured by the leng

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