Question

Mr. West is painting his front sidewalk to make it colorful. The total area is 24 square feet. What are the possible dimensions of the sidewalk? Be sure to create all possible combinations through representations and labels.

Answer 1

All possible dimensions are: 1ft × 24ft = 24
`ft^(2)`, 2ft × 12ft = 24
`ft^(2)`, 3ft × 8ft = 24
`ft^(2)`, 4ft × 6ft = 24
`ft^(2)`, 6ft × 4ft = 24
`ft^(2)`, 8ft × 3ft = 24
`ft^(2)`, 12ft × 2ft = 24
`ft^(2)`, or 24ft × 1ft = 24
`ft^(2)`.

Explanation:

With the assumption that the sidewalk has a rectangular shape:

Area of a rectangle = length × width

From the question, the total area = 24
`ft^(2)`.

⇒ length × width = 24
`ft^(2)`

So, all possible combinations are:

i. 1 ft × 24 ft = 24
`ft^(2)`

ii. 2 ft × 12 ft = 24
`ft^(2)`

iii. 3 ft × 8 ft = 24
`ft^(2)`

iv. 4ft × 6 ft = 24
`ft^(2)`

v. 6ft × 4ft = 24
`ft^(2)`

vi. 8ft × 3ft = 24
`ft^(2)`

vii. 12ft × 2ft = 24
`ft^(2)`

viii. 24ft × 1ft = 24
`ft^(2)`