SOLUTION: A square has an area that measures twice the area of a circle. Calculate the ratio of the perimeter of the square to the circumference of the circle.

Question 1051388: A square has an area that measures twice the area of a circle. Calculate the ratio of the perimeter of the square to the circumference of the circle.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let s be the side of the square and r be the radius of the circle, then
:
1) s^2 = 2*pi*r^2
:
Perimeter of square = 4s
:
Circumference of circle = 2*pi*r
:
from equation 1) s = square root (2*pi*r^2)
:
ratio of perimeter of square to circumference of the circle = (4*r*square root(2*pi)) / (2*pi*r) = (2*square root(2*pi)) / pi
:
square the numerator and denominator
:
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4 * 2 * pi / pi^2 = 8 / pi
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