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A rectangle with diagonal length x is twice as long as it is wide. Wha

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A rectangle with diagonal length x is twice as long as it is wide. Wha  [#permalink]

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New post 22 Mar 2019, 00:52
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

50% (02:16) correct 50% (02:01) wrong based on 36 sessions

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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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New post 22 Mar 2019, 04:01
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
IMO B
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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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New post 22 Mar 2019, 08:42
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
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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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New post 24 Mar 2019, 07:33
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?
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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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New post 24 Mar 2019, 18:43
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.

Answer: B
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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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