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Math Expert V
Joined: 02 Sep 2009
Posts: 59725
A rectangle with diagonal length x is twice as long as it is wide. Wha  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 58% (02:02) correct 42% (01:56) wrong based on 45 sessions

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A rectangle with diagonal length x is twice as long as it is wide. What is the area of the rectangle?

(A) x^2/4
(B) 2x^2/5
(C) x^2/2
(D) x^2
(E) 3x^2/2

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GMAT Club Legend  V
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Re: A rectangle with diagonal length x is twice as long as it is wide. Wha  [#permalink]

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Bunuel wrote:
A rectangle with diagonal length x is twice as long as it is wide. What is the area of the rectangle?

(A) x^2/4
(B) 2x^2/5
(C) x^2/2
(D) x^2
(E) 3x^2/2

l= 2y
width = y
d=x
so area = 2y^2
and digonal = √4y^2+y^2
x= √5y^2= y√5
y= x/√5
so
area= 2*y^2

2*x^2/5
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Joined: 02 Sep 2018
Posts: 27
Schools: Stanford MSx '21
Re: A rectangle with diagonal length x is twice as long as it is wide. Wha  [#permalink]

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1
Let width be y, hence length = 2y
Accordingly area = 2y^2

From the diagonal x, we get the relationship using y^2+4y^2 = x^2
Hence y^2=x^2/5
Area = 2*x^2/5
Ans B
Intern  B
Joined: 08 Dec 2018
Posts: 11
Location: India
Schools: ISB '20, IIMA PGPX"20
Re: A rectangle with diagonal length x is twice as long as it is wide. Wha  [#permalink]

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1
Bunuel wrote:
A rectangle with diagonal length x is twice as long as it is wide. What is the area of the rectangle?

(A) x^2/4
(B) 2x^2/5
(C) x^2/2
(D) x^2
(E) 3x^2/2

The language of this question indicates that length of the diagonal is twice the breadth. How you assumed that the length is twice the breadth?
Am I missing something, please clarify?
Target Test Prep Representative V
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Re: A rectangle with diagonal length x is twice as long as it is wide. Wha  [#permalink]

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1
Bunuel wrote:
A rectangle with diagonal length x is twice as long as it is wide. What is the area of the rectangle?

(A) x^2/4
(B) 2x^2/5
(C) x^2/2
(D) x^2
(E) 3x^2/2

We can let the length = 2w and width = w. Using the Pythagorean theorem we have:

(2w)^2 + w^2 = x^2

4w^2 +w^2 = x^2

5w^2 = x^2

w√5 = x

w = x/√5, so the length is 2x/√5, and the area is 2x^2/5.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: A rectangle with diagonal length x is twice as long as it is wide. Wha   [#permalink] 24 Mar 2019, 18:43
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