Find a Pythagorean triplet whose one member is 14.

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 = 14

⇒ m² = 14 + 1 = 15

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

If m² + 1 = 14

⇒ m² = 14 − 1 = 13

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

Therefore, let 2m = 14

⇒ m = 7, which is a natural number greater than 1

∴ m² − 1 = 7² − 1 = 49 − 1 = 48,

m² + 1 = 7² + 1 = 49 + 1 = 50.

Therefore, the required Pythagorean triplet is 14, 48 and 50.