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If the perimeter of a square is eight times its area, what is the diag

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If the perimeter of a square is eight times its area, what is the diag  [#permalink]

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New post 29 Aug 2018, 00:39
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

83% (01:12) correct 17% (01:25) wrong based on 23 sessions

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If the perimeter of a square is eight times its area, what is the diag  [#permalink]

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New post 29 Aug 2018, 00:47
Let a be the side of the square.

Then perimeter is 4a and area is \(a^2\)

Given 4a = 8\(a^2\)

Then a = \(\frac{1}{2}\)

Diagonal of a square is a\(\sqrt{2}\)

\(\frac{1}{2}\sqrt{2}\)

C is the answer.
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If the perimeter of a square is eight times its area, what is the diag  [#permalink]

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New post 29 Aug 2018, 00:50
Bunuel wrote:
If the perimeter of a square is eight times its area, what is the diagonal of the square?


A. 1/4

B. 1/2

C. \(\frac{\sqrt{2}}{2}\)

D. 2

E. \(2\sqrt{2}\)


Perimeter of square with side a=4a and it's area=\(a^2\)

Given, \(4a=8*a^2\)
Or \(a=\frac{4}{8}=\frac{1}{2}\)

Now, diagonal of square=\(\sqrt{2}*a=\sqrt{2}*\frac{1}{2}\)=\(\frac{\sqrt{2}}{2}\)

Ans. (C)
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If the perimeter of a square is eight times its area, what is the diag &nbs [#permalink] 29 Aug 2018, 00:50
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