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

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Math Expert
Joined: 02 Sep 2009
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If the perimeter of a square is eight times its area, what is the diag  [#permalink]

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29 Aug 2018, 00:39
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Difficulty:

25% (medium)

Question Stats:

80% (01:13) correct 20% (01:25) wrong based on 20 sessions

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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. $$2\sqrt{2}$$

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

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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$$\sqrt{2}$$

$$\frac{1}{2}\sqrt{2}$$

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

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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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