Question

A pool measuring 12 meters by 26 meters is surrounded by a path of uniform​ width, as shown in the figure. If the area of the pool and the path combined is 576 square​ meters, what is the width of the​ path?

The width of the path is __?__ meters

Answer 1

path width = 3 m

Explanation:

let x = the width of the path

(12 + 2x)(26 + 2x) = 576

312 + 24x + 52x + 4x² = 576

4x² + 76x - 264 = 0

divide both sides of the equation by 4:

x² + 19x - 66 = 0

(x + 22)(x - 3)= 0

x = 3 m