OG: If the length of a diagonal of a square is 2(root x), what is the area

[AbeNeedsAnswers]

If the length of a diagonal of a square is 2(root x), what is the area of the square in terms of x?

A. (root x)
B. (root 2x)
C. 2(root x)
D. x
E. 2x

E

[Brent@GMATPrepNow]

If the length of a diagonal of a square is 2(root x), what is the area of the square in terms of x?

A. (root x)
B. (root 2x)
C. 2(root x)
D. x
E. 2x

E

Here's what we're dealing with:


We're dealing with a right triangle
So, we can apply the Pythagorean theorem to write: k² + k² = (2√x)²
Simplify to get: 2k² = 4x
Divide both sides by 2 to get: k² = 2x

Since k = length of one side of the square, it follows that k² = the area of the square
Since k² = 2x, we can conclude that 2x = the area of the square.

Answer: E

Cheers,
Brent