## Task A-4.5. (4 points)

A rectangular path with a width of $1.5 \mathrm{~m}$ and a length of $20 \mathrm{~m}$ needs to be tiled with identical tiles in the shape of an isosceles right triangle with legs of length $50 \mathrm{~cm}$, such that the legs are parallel to the sides of the rectangle. Determine the number of ways this can be done.
## Solution.

It is clear that two triangles will form squares with a side length of 0.5.

There are $3 \cdot 40 = 120$ such squares.

Each of the smaller squares $0.5 \times 0.5$ can be tiled in two ways.
![](https://cdn.mathpix.com/cropped/2024_05_30_5dbbe9edfad2d8808b54g-27.jpg?height=206&width=498&top_left_y=865&top_left_x=787)

We conclude that the number of tilings is $2^{120}$.