Question

A rectangular swimming pool had a length twice as long as it’s width. The pool has a sidewalk around it that is 2 feet wide. Write an expression that would help you find the area of the pool and it’s sidewalk.

Answer 1

Area =
`2w^2+12w+16`

Explanation:

We let the width of the pool be "w"

We know the length is twice as long as width, so the length is:

2w

So,

Width = w

Length = 2w

Since a sidewalk with 2 feet width goes around the pool completely, the area enclosed by pool + sidewalk would have 2 feet around it, so its length and width would be:

Width = w + 2 + 2 = w + 4

Length = 2w + 2 + 2 = 2w + 4

The area of a rectangular region is always length * width, so the expression for area of pool and sidewalk would be:

`(w+4)(2w+4)\\=2w^2+4w+8w+16\\=2w^2+12w+16`

If we let the width of the swimming pool be "w", the expression for the area of pool and sidewalk is:

Area =
`2w^2+12w+16`