Question

Anthony is building a rectangular shaped swimming pool with a perimeter of 80 feet. Determine a function A(w) that models the area of the top surface of the swimming pool in terms of width W. A(w)= For w>0

Answer 1

`A(w) = 40w - w^2`

Explanation:

Given

`P = 80` --- perimeter

Required

Define the area in terms of width

The perimeter of the pool is:

`P =2(l + w)`

Where:

`l\to length`

`w\to width`

So:

`80 =2(l + w)`

Divide by 2

`40 =l + w`

Make l the subject

`l = 40-w`

The area is then calculated as;

`A(w) = l * w`

Substitute:
`l = 40-w`

`A(w) = (40 - w) * w`

`A(w) = 40w - w^2`