A right-angled triangle has sides that are in the ratio of $3: 4: 5$; what are the lengths of the sides of the triangle if its area is $24 \mathrm{~cm}^{2} ?$
The legs of the right-angled triangle in question are $3 x$ and $4 x$, and the hypotenuse is $5 x$.

According to our assumption, therefore:

$$
3 x \cdot 4 x = 48
$$

from which

$$
x = 4
$$

Thus, the sides of the triangle are 12, 16, and $20 \, \text{cm}$ long.