Respuesta :
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
