If the base is $a$, the side is $b$, and the heights are $m_{1}$ and $m_{2}$, then

$$
a+2 b=468,13 m_{2}=10 m_{1}, a m_{1}=b m_{2}
$$

from which $a=130 \mathrm{~cm}, b=169 \mathrm{~cm}$.

(Pál Füstös, Eger.)

The problem was also solved by: L. Bánó, E. Freund, Z. Harsányi, P. Heimlich, Gy. Jánosy, J. Kiss, A. Paunz, Sarolta Petrik, S. Pichler, Z. Reich, E. Sárközy, Gy. Schilhanek, Gy. Schlesinger, Gy. Schuster, J. Steiger, J. Szabó, B. Tóth.
An isosceles triangle has a perimeter of $468 \mathrm{~cm}$. The height corresponding to the leg is in the ratio of $10: 13$ to the height corresponding to the base. What are the lengths of the sides of the triangle?