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

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

by AbeNeedsAnswers » Fri Jun 05, 2020 6:31 pm

00:00

A

B

C

D

E

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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 [email protected] » Sat Jun 06, 2020 4:40 am
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: We're dealing with a right triangle
So, we can apply the Pythagorean theorem to write: k² + k² = (2√x
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.