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If a square region has area x, what is the length of its diagonal in

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If a square region has area x, what is the length of its diagonal in  [#permalink]

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New post 27 Sep 2017, 04:52
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

69% (00:27) correct 31% (00:19) wrong based on 25 sessions

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If a square region has area x, what is the length of its diagonal in  [#permalink]

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New post 27 Sep 2017, 05:56
Bunuel wrote:
If a square region has area x, what is the length of its diagonal in terms of x?

(A) √x
(B) √(2x)
(C) 2√x
(D) x√2
(E) 2x

Because \(s^2\) = area of a square:

\(s^2 = x\)
\(s = \sqrt{x}\)

A square's diagonal* is given by \(s\sqrt{2}\)

\(\sqrt{x} * \sqrt{2} = \sqrt{2x}\)

Answer B

*OR use Pythagorean theorem, where hypotenuse = diagonal = d

\((\sqrt{x})^2 + (\sqrt{x})^2 = d^2\)
\(2x = d^2\)
\(\sqrt{2x} = \sqrt{d^2}\)
\(d =\sqrt{2x}\)
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If a square region has area x, what is the length of its diagonal in &nbs [#permalink] 27 Sep 2017, 05:56
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