## 2. Square multiplication

If you increase one side of the square $K$ three times and the other side two times, you will get a rectangle $P$ whose area is $96 \mathrm{~cm}^{2}$. By how many millimeters is the perimeter of the rectangle $P$ greater than the perimeter of the square $K$?

## Result: 240
## Solution.

If we increase the length of one side by 3 times and the length of the other side by 2 times, the area will increase by 6 times.

Since the area of the obtained rectangle $\mathrm{P}$ is $96 \mathrm{~cm}^{2}$, it follows that the area of the square $K$ is 96:6=16 cm². Therefore, the length of the side of the square $K$ is $4 \mathrm{~cm}$, and its perimeter is $16 \mathrm{~cm}$.

![](https://cdn.mathpix.com/cropped/2024_05_30_b2fae673861d4dcd40e1g-3.jpg?height=451&width=651&top_left_y=174&top_left_x=705)

The lengths of the sides of the rectangle $P$ are $3 a=12 \mathrm{~cm}$ and $2 a=8 \mathrm{~cm}$, and its perimeter is $o=40 \mathrm{~cm}$.

The difference in the perimeters of the rectangle $P$ and the square $K$ is $40-16=24 \mathrm{~cm}$, i.e., the perimeter of the rectangle $P$ is $240 \mathrm{~mm}$ greater than the perimeter of the square $K$.