Question

A swimming pool 40 feet long and 24 feet wide is surrounded by a concrete sidewalk of uniform width x. The total area enclosed by the pool and sidewalk is 1380 square feet how long is the sidewalk along the length of the pool?

Answer 1

`46\ \text{feet}`

Explanation:

Let width of the sidewalk be
`x`

Area of the sidewalk and pool is 1380 square feet

So

`(40+2x)(24+2x)=1380\\\Rightarrow 960+128x+4x^2=1380\\\Rightarrow 4x^2+128x-420=0\\\Rightarrow x=(-128\pm √(128^2-4* 4\left(-420\right)))/(2* 4)\\\Rightarrow x=3,-35`

The width of the sidewalk is 3 feet.

The length of the side walk will be
`40+2x=40+2* 3=46\ \text{feet}`.