Answer:
Explanation:
To find two possibilities for the dimensions of the box with a volume of 108 cubic inches, where each side must be at least 3 inches long, you can start by listing the factors of 108. Then, you can pair up these factors to create dimensions that satisfy the given conditions.
The factors of 108 are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
Now, let's pair up these factors to create dimensions where each side is at least 3 inches long:
**Possibility 1:**
- Let one side be 3 inches.
- Let the second side be 3 inches.
- To achieve a volume of 108 cubic inches, the third side should be \(108 / (3 \times 3) = 12\) inches.
So, the dimensions for Possibility 1 are 3 inches by 3 inches by 12 inches.
**Possibility 2:**
- Let one side be 4 inches.
- Let the second side be 4 inches.
- To achieve a volume of 108 cubic inches, the third side should be \(108 / (4 \times 4) = 6.75\) inches.
However, since each side must be at least 3 inches long, you can't have a side that's 6.75 inches long. Therefore, there's no second possibility that meets all the given conditions.
So, the only valid dimensions are 3 inches by 3 inches by 12 inches for the box with a volume of 108 cubic inches, where each side must be at least 3 inches long.