Question

You are making a walkway around part of a swimming pool. The dimensions of the swimming pool are 18 and 25, while the dimensions of the walkway are x. Write a polynomial that expresses the area of the swimming pool.

Answer 1

`A = 4x^2 + 86x + 450`

Explanation:

Given

`Walkway = x`

`Length = 18`

`Width = 25`

Required:

The area of the swimming pool

Assume the walkway will be on the 4 sides of the swimming pool.

The total length (L) of the swimming pool will be:

`L = 18 + x + x`

`L = 18 + 2x`

The total width (W) will be:

`W = 25 + x + x`

`W = 25 + 2x`

The area (A) is:

`A = L * W`

`A = (18 + 2x) * (25 + 2x)`

Expand bracket

`A = 18 * 25 + 18 * 2x + 25 * 2x + 2x * 2x`

`A = 450 + 36x + 50x + 4x^2`

`A = 450 + 86x + 4x^2`

Reorder

`A = 4x^2 + 86x + 450`