community pool is adding a walkway around the perimeter of the pool. the walkway will have the same width on each side of the pool. the pool measures 22 meters by 10 meters and the area of the pool including the walkway will total 540 square meters.

The width of the walkway is 8m

Step-by-step explanation:

Given that,

Dimensions of pool is 22 x 10

The area of the pool including the walkway = 540 sq. meter

The area of the pool = 22 x 10

= 220 sq. meter

The area of the walkway = 540 - 220

= 320 sq. meter

The area of the pool with the walkway = 540 sq. meter

Let the width of the walkway be 'w'

Area = (22+w) (10+w)

540 = 220+22w+10w + (w^2)

540-220 = 32w + (w^2)

320 = (w^2) + 32w

(w^2) + 32w = 320

(w^2) + 32w - 320 = 0

Solving the quadratic equation by splitting the middle term.

(w^2) + 40w - 8w - 320 = 0

w (w+40) - 8 (w+40) = 0

(w+40) (w-8) = 0

w = 8 (or) - 40

The width cannot be negative so the width of the walkway is 8 meter