Write three sets of Pythagorean triplets such that each set has numbers less than `30`

Answer

To find three sets of Pythagorean triplets where each number is less than 30, we will follow the property of Pythagorean triplets, which states that for three positive integers \(a\), \(b\), and \(c\) (where \(c\) is the largest), the following equation must hold:

\[ a^2 + b^2 = c^2 \]

### Step-by-Step Solution:

1. **Identify the first triplet**:
- Let's take \(a = 3\) and \(b = 4\).
- Calculate \(c\):
\[ c = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]
- The first triplet is \((3, 4, 5)\).

2. **Identify the second triplet**:
- Now, let's take \(a = 5\) and \(b = 12\).
- Calculate \(c\):
\[ c = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \]
- The second triplet is \((5, 12, 13)\).

3. **Identify the third triplet**:
- For the third triplet, let's take \(a = 6\) and \(b = 8\).
- Calculate \(c\):
\[ c = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \]
- The third triplet is \((6, 8, 10)\).

### Summary of the Triplets:
- The three sets of Pythagorean triplets with numbers less than 30 are:
1. \((3, 4, 5)\)
2. \((5, 12, 13)\)
3. \((6, 8, 10)\)