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# A rectangle has length 2x and width x. If each diagonal of the rectang

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Math Expert
Joined: 02 Sep 2009
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A rectangle has length 2x and width x. If each diagonal of the rectang  [#permalink]

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05 Feb 2019, 03:02
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Difficulty:

35% (medium)

Question Stats:

75% (01:40) correct 25% (02:00) wrong based on 16 sessions

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A rectangle has length 2x and width x. If each diagonal of the rectangle has length d, what is the area of the rectangle, in terms of d?

A. 2d/5

B. 5d/2

C. 4d^2/25

D. 2d^2/5

E. 2d^2/3

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A rectangle has length 2x and width x. If each diagonal of the rectang  [#permalink]

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Updated on: 05 Feb 2019, 05:40
IMO D

$$d = \sqrt{4x^2 + x^2} = x\sqrt5$$
$$x=d/\sqrt5$$

Area = $$x*2x= 2x^2 = 2*d^2/5$$

---------------------------------------

Originally posted by GMATMBA5 on 05 Feb 2019, 05:19.
Last edited by GMATMBA5 on 05 Feb 2019, 05:40, edited 2 times in total.
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A rectangle has length 2x and width x. If each diagonal of the rectang  [#permalink]

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Updated on: 06 Feb 2019, 01:53
Bunuel wrote:
A rectangle has length 2x and width x. If each diagonal of the rectangle has length d, what is the area of the rectangle, in terms of d?

A. 2d/5

B. 5d/2

C. 4d^2/25

D. 2d^2/5

E. 2d^2/3

length 2x and width = x
area = 2x^2
diagonal = (2x)^2 + x^2= 5x^2= d^2
x^2=d^2/5
so
2* d^2/5
IMO D
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Originally posted by Archit3110 on 05 Feb 2019, 05:33.
Last edited by Archit3110 on 06 Feb 2019, 01:53, edited 1 time in total.
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Joined: 14 May 2018
Posts: 44
GMAT 1: 710 Q49 V38
Re: A rectangle has length 2x and width x. If each diagonal of the rectang  [#permalink]

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05 Feb 2019, 20:47
Bunuel wrote:
A rectangle has length 2x and width x. If each diagonal of the rectangle has length d, what is the area of the rectangle, in terms of d?

A. 2d/5

B. 5d/2

C. 4d^2/25

D. 2d^2/5

E. 2d^2/3

From pythagorus theorem, we have

d^2=x^2+(2x)^2
d^2=5(x)^2
==>x^2=d^2/5

Now,area = x*2x=2x^2=2d^2/5

Ans:D
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GMAT:710 (Q49,V38,IR8,AWA5)

Re: A rectangle has length 2x and width x. If each diagonal of the rectang   [#permalink] 05 Feb 2019, 20:47
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