A pool measuring 16 Meters by 28 m is surrounded by a path of uniform width, if the area of the pool and path combined is 748 m², what is the width of the path?

Answer: the width of the path is 3 meters.

Step-by-step explanation:

Let x represent the width of the path.

A pool measuring 16 meters by 28 meters is surrounded by a path of uniform width. It means that the combined length of the pool and the path is (16 + 2x) meters.

Also, the combined width of the pool and the path is (28 + 2x) meters.

if the area of the pool and the path combined is 748 square meters, it means that

(16 + 2x) (28 + 2x) = 748

448 + 32x + 56x + 4x² = 748

4x² + 88x + 448 - 748 = 0

4x² + 88x - 300 = 0

Dividing through by 4, it becomes

x² + 22x - 75 = 0

x² + 25x - 3x - 75 = 0

x (x + 25) - 4 (x + 25) = 0

x - 3 = 0 or x + 25 = 0

x = 3 or x = - 25

Since the width cannot be negative, then x = 3