Let the width of the path be represented by x.
The total width of the pool and the path would then be 16 + 2x (for the two shorter sides) and 28 + 2x (for the two longer sides).
The area of the pool itself is 16 × 28 = 448 square meters.
The area of the combined pool and path is 864 square meters.
So the area of just the path is:
864 - 448 = 416 square meters
The area of the path can also be expressed as the area of the larger rectangle (16 + 2x) × (28 + 2x) minus the area of the pool (16 × 28).
So we can set up the equation:
(16 + 2x) × (28 + 2x) - 448 = 416
Expanding the left side and simplifying:
4x^2 + 88x - 480 = 0
Dividing by 4:
x^2 + 22x - 120 = 0
Using the quadratic formula:
x = (-22 ± sqrt(22^2 - 4(-120)))/2
x = (-22 ± 26)/2
x = 2 or x = -24
The width of the path cannot be negative, so the width of the path is 2 meters.