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What is the perimeter of a square that has the same area as a circle

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What is the perimeter of a square that has the same area as a circle  [#permalink]

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New post 16 Nov 2017, 01:44
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

71% (01:49) correct 29% (01:44) wrong based on 93 sessions

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VP
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Posts: 1104
What is the perimeter of a square that has the same area as a circle  [#permalink]

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New post Updated on: 02 Jan 2018, 15:19
Bunuel wrote:
What is the perimeter of a square that has the same area as a circle that has circumference 1?

(A) 4√π
(B) 2/√π
(C) 1/(2√π)
(D) 1/π
(E) 1


π2r=1
r=1/2π
r^2=1/4π^2
πr^2=1/4π=s^2
s=√1/4π=1/2√π
4s=4/2√π=2/√π
B

Originally posted by gracie on 16 Nov 2017, 13:41.
Last edited by gracie on 02 Jan 2018, 15:19, edited 2 times in total.
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Re: What is the perimeter of a square that has the same area as a circle  [#permalink]

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New post 02 Jan 2018, 08:45
1
Bunuel wrote:
What is the perimeter of a square that has the same area as a circle that has circumference 1?

(A) 4√π
(B) 2/√π
(C) 1/(2√π)
(D) 1/π
(E) 1


Circumference \(= 2πr=1\) \(=> r=\frac{1}{2π}\)

Hence area of circle \(= πr^2=π(\frac{1}{2π})^2=\frac{1}{4π}\)

Given area of circle = area of square

or \(a^2=\frac{1}{4π} => a=\sqrt{\frac{1}{4π}}\)

Therefore \(a=\frac{1}{2\sqrt{π}}\)

Hence perimeter \(=4a=4*\frac{1}{2\sqrt{π}}=\frac{2}{\sqrt{π}}\)

Option B
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Re: What is the perimeter of a square that has the same area as a circle  [#permalink]

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New post 02 Jan 2018, 10:28
gracie wrote:
Bunuel wrote:
What is the perimeter of a square that has the same area as a circle that has circumference 1?

(A) 4√π
(B) 2/√π
(C) 1/(2√π)
(D) 1/π
(E) 1


π2r=1
r=1/2π
r^2=1/4π^2
πr^2=1/4π=s^2
s=√1/4π
4s=1/(2√π)
C


Hi gracie

the highlighted part is incorrect, hence you are getting C
VP
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Joined: 07 Dec 2014
Posts: 1104
Re: What is the perimeter of a square that has the same area as a circle  [#permalink]

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New post 02 Jan 2018, 14:36
niks18 wrote:
gracie wrote:
Bunuel wrote:
What is the perimeter of a square that has the same area as a circle that has circumference 1?

(A) 4√π
(B) 2/√π
(C) 1/(2√π)
(D) 1/π
(E) 1


π2r=1
r=1/2π
r^2=1/4π^2
πr^2=1/4π=s^2
s=√1/4π
4s=1/(2√π)
C


Hi gracie

the highlighted part is incorrect, hence you are getting C


hi niks18,
thank you for pointing out my error.
gracie
GMAT Club Bot
Re: What is the perimeter of a square that has the same area as a circle &nbs [#permalink] 02 Jan 2018, 14:36
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