To find the dimensions of a dog pen with an area of 150 square feet, where each side is at least 5 feet long and using whole number dimensions, we can set up the problem using the formula for the area of a rectangle:
\[ \text{Area} = \text{Length} \times \text{Width} \] \[ L \times W = 150 \]
Where:
- \( L \) is the length,
- \( W \) is the width.
Given the constraint that both \( L \) and \( W \) must be at least 5 feet, we can start checking pairs of factors of 150 that satisfy this condition.
The factors of 150 are:
- 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150.
However, since both dimensions must be at least 5, we will only consider pairs that meet this requirement.
Looking for pairs (L, W) such that both \( L \) and \( W \) are ≥ 5:
- \( 5 \times 30 = 150 \)
- Dimensions: (5, 30)
- \( 6 \times 25 = 150 \)
- Dimensions: (6, 25)
- \( 10 \times 15 = 150 \)
- Dimensions: (10, 15)
Here are the valid options for the dimensions of the dog pen which meet the criteria:
- \( L = 5 \), \( W = 30 \)
- \( L = 6 \), \( W = 25 \)
- \( L = 10 \), \( W = 15 \)
These can be arranged in reverse as well, yielding the following pairs:
- (30, 5)
- (25, 6)
- (15, 10)
So your friend can construct the dog pen with any of the following dimension pairs:
- 5 ft by 30 ft
- 6 ft by 25 ft
- 10 ft by 15 ft