Question

A friend is building a dog pen with an area of 150 square feet. Each side must be at least 5 feet long using only whole number dimensions

Answer 1

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:

1. \( 5 \times 30 = 150 \)
- Dimensions: (5, 30)
2. \( 6 \times 25 = 150 \)
- Dimensions: (6, 25)
3. \( 10 \times 15 = 150 \)
- Dimensions: (10, 15)

Here are the valid options for the dimensions of the dog pen which meet the criteria:

1. \( L = 5 \), \( W = 30 \)
2. \( L = 6 \), \( W = 25 \)
3. \( L = 10 \), \( W = 15 \)

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