Question 360055
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.