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

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Joined: 02 Sep 2009
Posts: 42648

Kudos [?]: 135946 [0], given: 12716

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, 03:52
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

68% (00:29) correct 32% (00:21) wrong based on 21 sessions

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Kudos [?]: 135946 [0], given: 12716

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Joined: 22 May 2016
Posts: 1137

Kudos [?]: 407 [0], given: 647

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, 04:56
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

\((\sqrt{x})^2 + (\sqrt{x})^2 = d^2\)
\(2x = d^2\)
\(\sqrt{2x} = \sqrt{d^2}\)
\(d =\sqrt{2x}\)

Kudos [?]: 407 [0], given: 647

If a square region has area x, what is the length of its diagonal in   [#permalink] 27 Sep 2017, 04:56
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If a square region has area x, what is the length of its diagonal in

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