## 2. Rectangles

Calculate the sum of all possible different perimeters that rectangles with an area of 144 and whose side lengths are natural numbers can have.

Result: $\quad 830$
## Solution.

The table below shows all possible dimensions for rectangles $a \times b$, along with the corresponding perimeter.

| $a$ | 1 | 2 | 3 | 4 | 6 | 8 | 9 | 12 |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| $b$ | 144 | 72 | 48 | 36 | 24 | 18 | 16 | 12 |
| Perimeter | 290 | 148 | 102 | 80 | 60 | 52 | 50 | 48 |

The sum of the perimeters is 830.