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

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by AbeNeedsAnswers » Fri Jun 05, 2020 6:31 pm
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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
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Re: OG: If the length of a diagonal of a square is 2(root x), what is the area

by Brent@GMATPrepNow » Sat Jun 06, 2020 4:40 am
AbeNeedsAnswers wrote: ↑
Fri Jun 05, 2020 6:31 pm
 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:
Image

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
Brent Hanneson - Creator of GMATPrepNow.com
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