AMC 12A 2003 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 be the area of the circle circumscribed about the triangle. Find A / B.

Answer Choices
A. \dfrac{9}{16}
B. \dfrac{3}{4}
C. \dfrac{27}{32}
D. \dfrac{3 \sqrt{6}}{8}
E. 1