Question

Determine a function a(w) that models the area of the top surface of the swimming pool in terms of the width , w

Answer 1

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

Explanation:

Given

`P = 80` ---- perimeter

Required

Write the area as a function of width

The perimeter of a rectangle is:

`P =2(l + w)`

Where

`l \to length\\ w \to width`

So, we have:

`80 = 2*(l+w)`

Divide by 2

`40 = l + w`

Make l the subject

`l =40 - w`

The area of a rectangle is:

`A = l * w`

Substitute:
`l =40 - w`

`A = (40 - w) * w`

Hence, the function is:

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