Pythagorean Triplets Definition
Pythagorean triplets are sets of three positive integers \(a\), \(b\), and \(c\) that satisfy the equation:
\[ a^2 + b^2 = c^2 \]
Here, \(c\) is the largest number, commonly referred to as the hypotenuse in a right triangle context.

Analyzing the Triplet 12, 6, 20
To determine if 12, 6, and 20 are Pythagorean triplets, we need to identify \(a\), \(b\), and \(c\).
- Assign values:
- \(a = 12\)
- \(b = 20\) (since it's the largest)
- \(c = 6\)

Calculating the Squares
We calculate the squares of these numbers:
- \(a^2 = 12^2 = 144\)
- \(b^2 = 20^2 = 400\)
- \(c^2 = 6^2 = 36\)

Verifying the Pythagorean Theorem
Now, check if the equation holds:
\[ a^2 + c^2 = b^2 \]
- Calculate:
- \(12^2 + 6^2 = 144 + 36 = 180\)
- Compare with \(20^2\):
- \(20^2 = 400\)
Since \(180 \neq 400\), it shows that 12, 6, and 20 do not form a Pythagorean triplet.

Conclusion
Thus, the numbers 12, 6, and 20 are **not** Pythagorean triplets as they do not satisfy the Pythagorean theorem condition \(a^2 + b^2 = c^2\).