In the picture, there is a square tile with a side length of $10 \mathrm{dm}$, which is composed of four identical rectangles and a small square. The perimeter of the small square is five times smaller than the perimeter of the entire tile.

Determine the dimensions of the rectangles.

(K. Pazourek)

![](https://cdn.mathpix.com/cropped/2024_04_17_a44687afde4ea037c0fdg-3.jpg?height=389&width=397&top_left_y=842&top_left_x=835)

Hint. Determine the side length of the small square.
The perimeter of the small square is five times smaller than the perimeter of the tile, so its side is also five times smaller than the side of the tile. The side of the small square thus measures

$$
10: 5=2(\mathrm{dm}) \text {. }
$$

At the same time, the length of the side of the tile is equal to the sum of the lengths of the side of the small square and two shorter sides of the rectangle. The shorter side of the rectangle thus measures

$$
(10-2): 2=4(\mathrm{dm}) .
$$

At the same time, the length of the side of the tile is equal to the sum of the lengths of the shorter and longer sides of the rectangle. The longer side of the rectangle thus measures

$$
10-4=6(\mathrm{dm}) \text {. }
$$

The dimensions of the rectangles are $4 \mathrm{dm} \times 6 \mathrm{dm}$.