SOLUTION: the perimeter of a square and circle are the same. what is the ratio between the area of the circle to the area of the square?

Question 1054050: the perimeter of a square and circle are the same. what is the ratio between the area of the circle to the area of the square?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Perimeter of square = 4s, where s is the length of a side
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Perimeter of a circle = 2*pi*r, where pi=(22/7) and r is the radius, then
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4s = 2*pi*r
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s = (pi*r) / 2
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Area of square is s^2 and Area of circle is pi*r^2, then
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(pi*r^2) / ((pi*r /2))^2 = (pi*r^2) / ((pi^2 * r^2)/4) =
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((pi*r^2) * 4) / (pi^2 * r^2) = 4 / pi = (4 * 7) / 22 = 28 / 22 = 14 / 11
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Ratio of Area of the circle to the Area of the square is 4 / pi
which is 14 / 11
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