Answer:
5 m
Step-by-step explanation:
The area of rectangle is given by:
A = Length × Breadth
Given, the length of pool + path = 20 +2x
Breadth of the pool + path = 8+2x
Area of pool and the path = 540 m²
⇒[tex](20+2x)(8+2x) = 540[/tex]
⇒[tex]160 +56 x + 4x^2 = 540\\ \Rightarrow 4x^2+56x-380=0\\ \Rightarrow x^2+14x-95=0\Rightarrow x^2+19x-5x-95=0 \Rightarrow x(x+19)-5(x+19)=0\\ \Rightarrow (x+19)(x-5)=0\\\Rightarrow x=-19 \text{ or } x =5[/tex]
The length cannot be negative. Therefore, the width of the path is 5 m.
