AMC 12 2003a Problem 11

A square and an equilateral triangle have the same perimeter. Let $A$ be the area of the circle circumscribed about the square and $B$ the area of the circle circumscribed around the triangle. Find $A/B$.

$\mathrm{(A) \ } \frac{9}{16} \mathrm{(B) \ } \frac{3}{4} \mathrm{(C) \ } \frac{27}{32} \mathrm{(D) \ } \frac{3\sqrt{6}}{8} \mathrm{(E) \ } 1$