Question

A pool measuring 16 meters by 18 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and th

path combined is 1224 square meters, what is the width of the path?
Equations for sides are
16x+2x
18+ 2x
Please help

Answer 1

width of the path = 9 m

Explanation:

(18+2x)(16+2x) = 1224

288+32x+36x+4x² = 1224

4x²+68x+288-1224 = 0

4x² +68x - 936 = 0

4(x² +17x - 234) = 0

use quadratic formula to solve for x: (a=1, b=17,c=-234)

x = 9, -26 disregard the negative root

x=9

Alternate solution:

2(18x) +2(16x) + 4x² = 1224 - 288 = 936

solve for x

x=9