Question

You are building a walkway of uniform width around a 100 foot by 60 foot pool. After completing the walkway, you want to put a fence around the outer edge of the walkway. You have 450 feet of fencing to enclose the walkway. What is the maximum width of the walkway?

Answer 1

16.25 ft

Explanation:

Given: Width of walkway around pool is 100 foot by 60 foot.

Total fencing to enclose walkway is 450 ft.

Now, finding the value of maximum width of walkway around pool.

Lets assume the maximum width of walkway is "x".

Each dimension of the pool will have width added to
`x+x= 2x`

∴ Total measurement of dimension of walkway is
`(2x+100)\ by\ (2x+60)`

Next, we know total fencing will be equal to the perimeter of walkway area.

`2(l+w)= 450`

subtituting the value of length and width of walkway.

⇒
`2[(2x+100)+(2x+60)]= 450`

Opening parenthesis.

⇒
`2(4x+160)= 450`

dividing 2 both side.

⇒
`4x+160= 225`

Subtracting 160 both side

⇒
`4x= 65`

Cross multiplying

⇒ x=
`(65)/(4) = 16.25\ ft`

∴ Maximum width of walkway is 16.25 ft.