AHSME 1970 Problem 2

A square and a circle have equal perimeters. The ratio of the area of the circle to the are of the square is $\text{(A) } \frac{4}{\pi} \text{(B) } \frac{\pi}{\sqrt{2}} \text{(C) } \frac{4}{1} \text{(D) } \frac{\sqrt{2}}{\pi} \text{(E) } \frac{\pi}{4}$