An equilateral triangle has an area of $100 \mathrm{~cm}^{2}$. A circle is circumscribed around this triangle, and a square is inscribed in the circle. What is the area of the square?
Let the area of the regular triangle inscribed in a circle of radius $r$ be denoted by $t_{1}$ and the area of the inscribed square by $t_{2}$, then

$$
t_{1}=\frac{3 \sqrt{3}}{4} \quad \text { and } \quad t_{2}=2 r^{2}
$$

or

$$
t_{2}=\frac{8 t_{1}}{3 \sqrt{3}}
$$

In this example, $t_{1}=100$, so

$$
t_{2}=\frac{800}{3 \sqrt{3}}=153.96 \mathrm{~cm}^{2}
$$

(József Kiss, Pápa.)

Number of solutions: 20.