A pool measuring 18 meters by 22 meters is surrounded by a path of uniform width. If the area of the pool and the path combined is 1440 square meters, what is the width of the path?

the width of the uniform path is 9 meters.

Step-by-step explanation:

Let x represent the width of the uniform path.

A pool measuring 18 meters by 22 meters is surrounded by a path of uniform width. It means that the combined length of the pool and the uniform path is (18 + 2x) meters and the combined width of the pool and the uniform path is (22 + 2x) meters.

If the area of the pool and the path combined is 1440 square meters, it means that

(18 + 2x)(22 + 2x) = 1440

396 + 36x + 44x + 4x² = 1440

4x² + 80x + 396 - 1440 = 0

4x² + 80x - 1044 = 0

Dividing both sides of the equation by 4, it becomes

x² + 20x - 261 = 0

x² + 29x - 9x - 261 = 0

x(x + 29) - 9(x + 29) = 0

x - 9 = 0 or x + 29 = 0

x = 9 or x = 29

Since the width cannot be negative, then x = 9 meters