SOLUTION: A square and a circle have equal areas. Which shape has shorter perimeter?

Question 360055: A square and a circle have equal areas. Which shape has shorter perimeter?
Answer by Jk22(389) (Show Source): You can put this solution on YOUR website!
L=square side length, R=Circle radius

Area(Square) = L*L = Area(Circle) = Pi*R*R => R = L / Sqrt(Pi)

Perimeter(Square) = 4L, Perimeter(Circle) = 2Pi*R = 2Sqrt(Pi)*L

but we know that Sqrt(Pi) < 2, hence the perimeter of the circle is smaller.

Indeed since Pi<4, it's root is smaller than 2.
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