Question

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?

Answer 1

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.