The size of a television screen is given as the length of the screen’s diagonal. If the screens were flat, then the area

[Vincen]

The size of a television screen is given as the length of the screen’s diagonal. If the screens were flat, then the area of a square 21-inch screen would be how many square inches greater than the area of a square 19-inch screen?

A. 2
B. 4
C. 16
D. 38
E. 40

Answer: E

Source: GMAT Prep

[Brent@GMATPrepNow]

The size of a television screen is given as the length of the screen’s diagonal. If the screens were flat, then the area of a square 21-inch screen would be how many square inches greater than the area of a square 19-inch screen?

A. 2
B. 4
C. 16
D. 38
E. 40

Answer: E

Source: GMAT Prep

Let x be the length (and width) of the square screen with diagonal 21
The area of the large screen will be x²

Let y be the length (and width) of the square screen with diagonal 19
The area of the small screen will be y²

Our goal is to find the value of x² - y²

Large TV: If we examine the right triangle created by 2 sides (both with length x) and the diagonal, we can apply the Pythagorean Theorem to get x² + x² = 21²
When we simplify this, we get 2x² = 441, which means x² = 441/2

Small TV: If we examine the right triangle created by 2 sides (both with length y) and the diagonal, we can apply the Pythagorean Theorem to get y² + y² = 19²
When we simplify this, we get 2y² = 361, which means y² = 361/2

We can now find the value of x² - y²
We get x² - y² = 441/2 - 361/2 = 80/2 = 40

Answer: E

Cheers,
Brent