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

Question

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

gracie · Answer

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

niks18 · Answer

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

niks18 · Answer

Hi  gracie

the highlighted part is incorrect, hence you are getting C

gracie · Answer

hi niks18,
thank you for pointing out my error.
gracie

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