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

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Math Expert
Joined: 02 Sep 2009
Posts: 44421
What is the perimeter of a square that has the same area as a circle [#permalink]

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16 Nov 2017, 01:44
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Difficulty:

45% (medium)

Question Stats:

64% (01:20) correct 36% (00:58) wrong based on 88 sessions

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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
[Reveal] Spoiler: OA

_________________
Director
Joined: 07 Dec 2014
Posts: 929
What is the perimeter of a square that has the same area as a circle [#permalink]

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16 Nov 2017, 13:41
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

Last edited by gracie on 02 Jan 2018, 15:19, edited 2 times in total.
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1016
Location: India
GPA: 3.82
Re: What is the perimeter of a square that has the same area as a circle [#permalink]

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02 Jan 2018, 08:45
1
KUDOS
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
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1016
Location: India
GPA: 3.82
Re: What is the perimeter of a square that has the same area as a circle [#permalink]

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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
Director
Joined: 07 Dec 2014
Posts: 929
Re: What is the perimeter of a square that has the same area as a circle [#permalink]

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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
Re: What is the perimeter of a square that has the same area as a circle   [#permalink] 02 Jan 2018, 14:36
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