Problem 4. In the rectangle $A B C D$, the segments $A C$ and $B D$ intersect at point $O$. Determine the area of the rectangle if the distance from point $O$ to the longer side is 3 times less than the distance from point $O$ to the shorter side, and the perimeter of the rectangle is 128 cm.
Solution. Let the distance from point $O$ to the larger side be $x$. Then the distance from point $O$ to the smaller side is $3x$. Therefore, the sides of the rectangle are $6x$ and $2x$. Thus, $8x=64$, i.e., $x=8$. According to

![](https://cdn.mathpix.com/cropped/2024_06_05_4fa80d9916883368a7a6g-4.jpg?height=235&width=413&top_left_y=1094&top_left_x=1055)
this, the sides of the rectangle are $48 \mathrm{~cm}$ and $16 \mathrm{~cm}$, so the area is $48 \cdot 16 = 768 \mathrm{~cm}^{2}$.

## VII Section