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

1. Let the common perimeter be $P$. The hexagon has side $\frac P6$, and its circumradius equals its side length, so $A=\pi\left(\frac P6\right)^2=\frac{\pi P^2}{36}$.
2. The triangle has side $\frac P3$, and its circumradius is $\frac{1}{\sqrt3}\cdot\frac P3=\frac{P}{3\sqrt3}$, so $B=\pi\cdot\frac{P^2}{27}$.
3. $A/B=\frac{P^2/36}{P^2/27}=\boxed{\frac34}$.