smc

Let the radius of the circle be $r$. That means the diameter of the circle is $2r$, so the side length of the square is $r\sqrt{2}$. Therefore, the area of the square is $2r^2$. By using 30-60-90 triangles, half of the side length of an equilateral triangle is $r\sqrt{3}$, so each side is $2r\sqrt{3}$ units long. Thus, the area of the equilateral triangle is $3r^2\sqrt{3}$. The ratio of the area of the equilateral triangle to the area of the square is $\frac{3r^2\sqrt{3}}{2r^2}=\frac{3\sqrt{3}}{2}$, so the answer is $\boxed{3\sqrt{3}:2}$.