Problem 5. Three regular pentagons have a common center, their sides are respectively parallel. The sides of two pentagons are 4 cm and 12 cm. The third pentagon divides the area of the figure enclosed between the first two in the ratio $1: 3$, counting from the smaller pentagon. Find the side of the third pentagon.
Answer: $4 \sqrt{3}$.

Solution: Let the side of the third pentagon be $x$. The areas of similar figures are in the ratio of the squares of corresponding sides. Therefore, the areas enclosed between the pentagons are in the ratio $\left(x^{2}-4^{2}\right):\left(12^{2}-x^{2}\right)=1: 3$, from which the answer follows.