Find the Pythagorean triplet whose smallest number is 12.

Answer

To find the Pythagorean triplet whose smallest number is 12, we can use the formula for generating Pythagorean triplets. The smallest number in a Pythagorean triplet can be expressed as \(2m\), where \(m\) is a positive integer.

### Step-by-Step Solution:

1. **Identify the smallest number**: We know the smallest number in the triplet is 12.

2. **Set up the equation**: Since the smallest number is given by \(2m\), we can set up the equation:
\[ 2m = 12 \]

3. **Solve for \(m\)**: Divide both sides of the equation by 2 to find \(m\):
\[ m = \frac{12}{2} = 6 \]

4. **Calculate the other two numbers in the triplet**:
- The second number can be calculated using the formula \(m^2 - 1\):
\[ m^2 - 1 = 6^2 - 1 = 36 - 1 = 35 \]
- The third number can be calculated using the formula \(m^2 + 1\):
\[ m^2 + 1 = 6^2 + 1 = 36 + 1 = 37 \]

5. **Write the triplet**: The Pythagorean triplet is then:
\[ (12, 35, 37) \]

### Final Answer:
The Pythagorean triplet whose smallest number is 12 is \( (12, 35, 37) \).

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