A pool measuring 20 meters by 28 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 1584 square meters, what is the width of the path?

X = width of the path.

we can suggest this equation:

(20+2x) (28+2x) = 1584

we solve this equation:

(20+2x) (28+2x) = 1584

560+40x+56x+4x²=1584

4x²+96x-1024=0

4/4x²+96/4x-1024/4=0/4

x²+24x-256=0

We solve this square equation:

x=[-24⁺₋√ (576+1024) ]/2 = (-24⁺₋40) / 2

we have two solutions:

x₁ = (-24-40) / 2=-32 this solution is not valid.

x₂ = (-24+40) / 2=8

Answer: the width of the path is 8 m.