Question

A rectangle pool is 8 m longer than it is wide. A walkway is 2 m wide and it's around the pool. What is the dimensions of the pool of the area of the walkway is 176 m²

Answer 1

length=15.85m . width= 7.85m

Explanation:

Given the rectangle pool is 8m longer than its width.

Let the width of the rectangle be x , now the length of the rectangle pool is x+8

Also given there is a walkway of 2m wide in all the directions So the length of the pool and the width increases by 2m

Now length = x+10 and width = x+2

given the area of the rectangle = 176
`m^(2)`

The area of the pool=
`length* width`

Now
`(x+10)*(x+2)=176`

`x^(2) +12x+20=176`

`x^(2) +12x-156=0`

`x=\frac{-12 +\sqrt{12^(2)-4* 1 * (-156) } }{2* 1}`

on solving we get x=7.85m

Now the length is x+8=15.85m