Problem 4. The sum of all sides of two squares is $96 \mathrm{~cm}$. If the side of one square is three times larger than the side of the other square, then calculate the lengths of the sides of the two squares.
Solution. First method. Since the side of the larger square is three times larger than the side of the smaller square, the sum of one side of both squares is four times larger than the side of the smaller square. However, a square has four sides, so the sum of the sides of both squares is $4 \cdot 4=16$ times larger than the side of the smaller square. Therefore, the side of the smaller square is $96: 6=16 \mathrm{~cm}$. Then the side of the larger square is $6 \cdot 3=18 \mathrm{~cm}$.

Second method. Let $x$ be the length of the side of the smaller square. Then the length of the side of the larger square is $3 x$, so

$$
4 x+4 \cdot 3 x=96, \text { i.e. } x=6 \mathrm{~cm} \text {. }
$$

Thus, the side of the smaller square is $6 \mathrm{~cm}$, and the side of the larger square is $3 \cdot 6=18 \mathrm{~cm}$.

## V section