Final answer:
To find the width of the path, subtract the area of the pool from the total area of the pool and path combined. Then, divide the remaining area by the length of the pool to find the width of the path. The width of the path is approximately 29.27 meters.
Step-by-step explanation:
To find the width of the path, we need to find the difference between the total area of the pool and path combined and the area of just the pool. The area of the pool is equal to the length multiplied by the width. In this case, the area of the pool is 10 meters multiplied by 22 meters, which is equal to 220 square meters. So, if the area of the pool and path combined is 864 square meters, then the area of just the path is 864 square meters minus 220 square meters, which is equal to 644 square meters.
Now, we know that the path has a uniform width, so we can find the width of the path by dividing the area of the path by the length of the pool. In this case, the width of the path is 644 square meters divided by 22 meters, which is equal to 29.27 meters. Therefore, the width of the path is approximately 29.27 meters.