Task 1. A grass path surrounds a rectangular asphalt playground with dimensions $36 \mathrm{dm}$ and $12 \mathrm{~m}$ (as shown in the diagram). The width $d$ of the path is equal to a quarter of the semiperimeter of the playground. How many meters of wire are needed to fence the grass path around the playground, if it is surrounded by 5 rows of wire? How many posts are needed to secure the fence, if the distance between any two adjacent posts is $6 \mathrm{dm}$?
Solution. We have, $12 \mathrm{dm}=120 \mathrm{dm}$. The width of the path is

$$
d=(120+36): 4, d=39 \mathrm{dm}
$$

![](https://cdn.mathpix.com/cropped/2024_06_05_9d1696c7fd1a2cbf5bb5g-03.jpg?height=423&width=565&top_left_y=276&top_left_x=914)

Thus, one side of the lawn is $2 \cdot 39+120=198 \mathrm{dm}$ long, and the other side is $2 \cdot 39+36=114 \mathrm{dm}$ long.

To fence one row around the lawn, the following is needed:

$$
2(198+114)+2(120+36)=624+312=936 \mathrm{dm}
$$

Since it needs to be circled 5 times, $5 \cdot 936=4680 \mathrm{dm}$, i.e., 468 meters of wire are needed.

For securing the fence, 936:6=156 posts are needed.