State true/false:

The numbers 12, 35 and 37 form a Pythagorean triplet.

The given statement is true.

We know that the Pythagorean triplets can be found by using the general form 2m, m² − 1, m² + 1, where m is a natural number greater than 1.

If m² − 1 = 12

⇒ m² = 12 + 1 = 13

Then, the value of m will not be an integer.

If m² + 1 = 12

⇒ m² = 12 − 1 = 11

Then, the value of m will not be an integer.

Therefore, let 2m = 12

⇒ m = 6, which is a natural number greater than 1

∴ m² − 1 = 6² − 1 = 36 − 1 = 35,

m² + 1 = 6² + 1 = 36 + 1 = 37,

Therefore, the required Pythagorean triplet is 12, 35 and 37.