Question

The pool at your campsite measures 8 meters by 20 meters. It is surrounded by a path of uniform width, as shown in the figure. The area of the pool AND the path combined is 540 square meters. Write and solve an equation to fund the width of the path.​

Answer 1

5 m

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

⇒
`(20+2x)(8+2x) = 540`

⇒
`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`

The length cannot be negative. Therefore, the width of the path is 5 m.