(ii) If one number of the Pythagorean triplet is 9, then find the triplet

A Pythagorean triplet consists of three positive integers a, b, and c, such that a² + b² = c².

Given that one of the numbers is 9, we have two scenarios:

1. 9 is the hypotenuse (c). In this case, we need to find a and b such that a² + b² = 9² = 81. There are no two positive integers a and b that satisfy this equation, so there are no Pythagorean triplets where 9 is the hypotenuse.

2. 9 is either a or b. In this case, we need to find the other two numbers such that 9² + b² = c² or a² + 9² = c². The only Pythagorean triplets that satisfy these equations are (9, 40, 41) and (9, 12, 15).

So, the Pythagorean triplets that include the number 9 are (9, 40, 41) and (9, 12, 15).