Problem 3. The side of a regular polygon is 1 cm long. What is the perimeter of this regular polygon if it has 252 diagonals?
Solution. Let the regular polygon have $n$ sides. Then the number of its diagonals is $\frac{n(n-3)}{2}=252$, that is,

$$
n(n-3)=2^{3} \cdot 3^{2} \cdot 7=24 \cdot 21
$$

It follows that $n=24$, and the perimeter is $24 \mathrm{~cm}$.