## 7. Perimeter of a Rectangle

Rectangle $A B C D$ is composed of nine identical rectangles. The perimeter of each of these nine rectangles is $204 \mathrm{~cm}$.

Calculate the perimeter of rectangle $A B C D$ in centimeters.

![](https://cdn.mathpix.com/cropped/2024_05_30_44689c7bad1ce05a818cg-4.jpg?height=345&width=480&top_left_y=2256&top_left_x=1381)
## Solution.

The longer side of each of these nine rectangles is five times longer than the shorter side. If we divide the perimeter of one of them by 12, we get the length of the shorter side of each of these nine rectangles.

The shorter side has a length of $204: 12=17 \mathrm{~cm}$ and appears:

- in the sides $\overline{B C} \mathrm{and} \overline{A D}$ of rectangle $A B C D$ a total of $5+5$, i.e., 10 times,
- in the sides $\overline{A B}$ and $\overline{C D}$ of rectangle $A B C D$ a total of $9+9$, i.e., 18 times.

The shorter side of length $17 \mathrm{~cm}$ appears in the perimeter of rectangle $A B C D$ a total of $10+18$, i.e., 28 times.

The perimeter of rectangle $A B C D$ is $28 \cdot 17$, i.e., $476 \mathrm{~cm}$.