7. The area of a rectangle whose side lengths are expressed in centimeters as natural numbers is $48 \mathrm{~cm}^{2}$. What can be the area of a square whose perimeter is equal to the perimeter of the rectangle if the side length of the square is a natural number in centimeters?

No use of a pocket calculator or any reference materials is allowed.
7. Rectangle:

$P=48 \mathrm{~cm}^{2}$

$P=a \cdot b$

The table shows all possible values for the lengths of sides $a$ and $b$, and the perimeter is calculated.

| $a(\mathrm{~cm})$ | 1 | 2 | 3 | 4 | 6 |
| :---: | :---: | :---: | :---: | :---: | :---: |
| $b(\mathrm{~cm})$ | 48 | 24 | 16 | 12 | 8 |
| Perimeter (cm) | 98 | 52 | 38 | 32 | 28 |

Note 1: For each written case and calculated perimeter, 1 POINT is awarded.

Square:

For each of the 5 cases found, check if the length of side $a$ is a natural number:

| Perimeter (cm) | 98 | 52 | 38 | 32 | 28 |
| :---: | :---: | :---: | :---: | :---: | :---: |
| $a(\mathrm{~cm})$ | no solution | 13 | no solution | 8 | 7 |
| Area $\left(\mathrm{cm}^{2}\right)$ | - | 169 | - | 64 | 49 |

Note 2: For each written case and calculated area, 1 POINT is awarded.