Answer: 2 meters.
Step-by-step explanation:
Let w = width of the cement path.
Dimensions of pool : Length = 15 meters , width = 9 meters
Area of pool = length x width = 15 x 9 = 135 square meters
Along width cement path, the length of region = [tex]2w+15[/tex]
width = [tex]2w+9[/tex]
Area of road with pool = [tex](2w+15) (2w+9)[/tex]
[tex]= 4w^2+30w+18w+135\\\\=4w^2+48w+135[/tex]
Area of road = (Area of road with pool ) -(area of pool)
[tex]\Rightarrow\ 112 =4w^2+48w+135- 135\\\\\Rightarrow\ 112= 4w^2+48w\\\\\Rightarrow\ 4 w^2+48w-112=0\\\\\Rightarrow\ w^2+12w-28=0\ \ \ [\text{Divide both sides by 4}]\\\\\Rightarrow\ w^2+14w-2w-28=0\\\\\Rightarrow\ w(w+14)-2(w+14)=0\\\\\Rightarrow\ (w+14)(w-2)=0\\\\\Rightarrow\ w=-14\ or \ w=2[/tex]
width cannot be negative, so w=2 meters
Hence, the width of the road = 2 meters.
