Question
Matt and his dad are building a tree house. They buy enough flooring material to cover an area of 36 square feet. What are all possible dimensions of the floor?
Answers
Answered by
GPT-4o mini
To find all possible dimensions of the floor that can cover an area of 36 square feet, we need to consider the pairs of factors of 36. The area of a rectangle (or any shape with a floor) is calculated by multiplying its length and width.
Let's determine the factor pairs of 36:
1. \(1 \times 36 = 36\)
2. \(2 \times 18 = 36\)
3. \(3 \times 12 = 36\)
4. \(4 \times 9 = 36\)
5. \(6 \times 6 = 36\)
Thus, the possible dimensions (length and width) for the tree house floor can be represented as:
1. \(1 \text{ ft} \times 36 \text{ ft}\)
2. \(2 \text{ ft} \times 18 \text{ ft}\)
3. \(3 \text{ ft} \times 12 \text{ ft}\)
4. \(4 \text{ ft} \times 9 \text{ ft}\)
5. \(6 \text{ ft} \times 6 \text{ ft}\) (square)
These pairs represent all the possible dimensions that would result in a total area of 36 square feet.
Let's determine the factor pairs of 36:
1. \(1 \times 36 = 36\)
2. \(2 \times 18 = 36\)
3. \(3 \times 12 = 36\)
4. \(4 \times 9 = 36\)
5. \(6 \times 6 = 36\)
Thus, the possible dimensions (length and width) for the tree house floor can be represented as:
1. \(1 \text{ ft} \times 36 \text{ ft}\)
2. \(2 \text{ ft} \times 18 \text{ ft}\)
3. \(3 \text{ ft} \times 12 \text{ ft}\)
4. \(4 \text{ ft} \times 9 \text{ ft}\)
5. \(6 \text{ ft} \times 6 \text{ ft}\) (square)
These pairs represent all the possible dimensions that would result in a total area of 36 square feet.