Question

A rectangular swimming pool has a length twice as long as its 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 its sidewalk.

Answer 1

`A_p=2w^2`

`A_s=12w+16`

Explanation:

Functions and Geometry

Sometimes we need to express areas, volumes, and distances in terms of unknown quantities (or variables). When we can find such expressions, they can be referred to as functions. Let's recall the area of a rectangle is A=wl, being w its wide and l its length

Please refer to the image below. The length of the swimming pool is l and its width is w. Its area is

`A_p=lw`

We know the length is twice as long as its width, l=2w, so

`A_p=(2w)w=2w^2`

`A_p=2w^2`

The sidewalk is 2 feet wide. The length of the pool and its sidewalk is

`l'=l+4`

Similarly, the width of the pool+sidewalk is

`w'=w+4`

The area of the pool+sidewalk is

`A'=l'w'=(l+4)(w+4)=lw+4l+4w+16`

We know that l=2w, so

`A'=(2w)w+4(2w)+4w+16`

`A'=2w^2+12w+16`

The area of the sidewalk alone is the subtraction of both areas

`A_s=A'-A_p=2w^2+12w+16-2w^2`

Simplifying

`A_s=12w+16`