4. Determine the lengths of the legs of a right triangle with an area of $24 \mathrm{~cm}^{2}$. The lengths of the legs are natural numbers expressed in centimeters. Write all solutions.
4. Let $a$ and $b$ be the lengths of the legs of a right triangle, $a \leq b$.

The area of the right triangle is given by $P=\frac{a \cdot b}{2}$.

Substitute the given area:

$24=\frac{a \cdot b}{2} / \cdot 2$

$a \cdot b=48$

$1 \text{ POINT}$

All possible solutions are given in the table:

| $a(\mathrm{~cm})$ | 1 | 2 | 3 | 4 | 6 |
| :---: | :---: | :---: | :---: | :---: | :---: |
| $b(\mathrm{~cm})$ | 48 | 24 | 16 | 12 | 8 |
|  | 1 POINT | 1 POINT | 1 POINT | 1 POINT | 1 POINT |