Answer: 13 meters
Explanation:
To find the width of the path surrounding the pool, we can follow these steps:
1. Let's assume the width of the path is 'w'. This means that the dimensions of the pool (without the path) would be reduced by 2w on each side.
2. The length of the pool (without the path) would be reduced to 18 - 2w meters, and the width would be reduced to 22 - 2w meters.
3. The area of the pool (without the path) can be calculated by multiplying the length and width:
Area of pool = (18 - 2w) * (22 - 2w)
4. The total area of the pool and the path combined is given as 1020 square meters. So, we can set up the equation:
Area of pool + Area of path = 1020
(18 - 2w) * (22 - 2w) + (2w * 2w) = 1020
5. Simplify the equation:
(18 - 2w) * (22 - 2w) + 4w^2 = 1020
6. Expand and rearrange the equation:
396 - 40w + 4w^2 + 4w^2 = 1020
8w^2 - 40w + 396 - 1020 = 0
8w^2 - 40w - 624 = 0
7. Solve the quadratic equation. In this case, it can be factored:
(2w - 26)(4w + 24) = 0
8. Set each factor equal to zero and solve for 'w':
2w - 26 = 0 or 4w + 24 = 0
2w = 26 or 4w = -24
w = 13 or w = -6
9. Since the width of the path cannot be negative, we discard the solution w = -6.
Therefore, the width of the path surrounding the pool is 13 meters.