Uncle Ferda had two gardens: the carrot garden was square, and the strawberry garden was rectangular. The width of the strawberry garden was three times smaller than the width of the carrot garden, and the length of the strawberry garden was 8 meters longer than the length of the carrot garden.

When Uncle Ferda fenced the gardens, he found that both had the same perimeter. Determine the dimensions of the carrot and strawberry gardens.

(E. Novotná)
The strawberry garden was square, so its length was the same as its width, and this dimension was equal to three times the width of the strawberry garden. From the problem, we also know that the length of the strawberry garden was 8 meters longer than three times its width.
![](https://cdn.mathpix.com/cropped/2024_04_17_688753f95afb2ec1896eg-2.jpg?height=390&width=962&top_left_y=726&top_left_x=547)

The perimeters of both gardens expressed in terms of the width of the strawberry garden were:

perimeter of the carrot garden $=12 \times$ width of the strawberry garden,

perimeter of the strawberry garden $=8 \times$ width of the strawberry garden + 16 meters.

Since both gardens had the same perimeter, it followed that

$$
12 \times \text { width of the strawberry garden }=8 \times \text { width of the strawberry garden }+16 \text { meters. }
$$

From this, it follows that the width of the strawberry garden was $16: 4=4$ meters. Thus, the dimensions of the carrot garden were $12 \times 12$ meters and the dimensions of the strawberry garden were $20 \times 4$ meters.

Scoring suggestion. 2 points for expressing the length of the strawberry garden in terms of its width; 2 points for expressing the perimeters of both gardens; 1 point for expressing the width of the strawberry garden; 1 point for the dimensions of both gardens.