In a triangle, the base is $4 \mathrm{~cm}$ larger than the corresponding height. If we increase both the base and the height by $12 \mathrm{~cm}$, we get a triangle whose area is five times the area of the original triangle. What are the base and height of the original triangle?
Let the base of the triangle be $a$, then its height is $m=a-4$. According to the problem,

$$
(a+12)(a+8)=5 a(a-4)
$$

or

$$
a^{2}-10 a-24=0
$$

from which the positive root is: $a=12 \text{ cm}$, so $m=8 \text{ cm}$.

(Leó Spitzer, Budapest.)

The problem was also solved by: Bauer E., Breuer P., Dénes M., Döri V., Engler J., Erdős V., Fried E., Grün E., Grünwald M., Klein G., Koffer B., Köhler I., Lengyel K., Lengyel P., Neumann L., Rosenthal M., Rosinger J., Schnabel L., Sichermann F., Steiner L., Stolzer I., Szántó L., Szilárd V., Vilcsek A., Viola R., Wellis E.