Challenege question circle word problem

Question

A square and a circle have equal perimeters. Determine the ratio of the area of the circle to the area of the square in terms of pi.

Answer 1

Perimeter of a circle (C) = 2*pi*r, r =C/2pi, A_C = pi*r² = pi(C/2pi)² = C² /4pi

Perimeter of a square (P) = 4s, s = P/4, A_S = s² = P² /16

Set C = P, and then divide the expressions for area---A_C / A_S