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

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Math Expert
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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27 Sep 2017, 03:52
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68% (00:29) correct 32% (00:21) wrong based on 21 sessions

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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
[Reveal] Spoiler: OA

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

VP
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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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 $$s\sqrt{2}$$

$$\sqrt{x} * \sqrt{2} = \sqrt{2x}$$

*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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