Identify, with reason, which of the following are Pythagorean triplets.

(i) (3, 5, 4) (ii) (4, 9, 12)

(iii) (5, 12, 13) (iv) (24, 70, 74)

(v) (10, 24, 27) (vi) (11, 60, 61)

In a triangle with sides (a,b,c), the Pythagoran’s theorem states that

a² + b² = c². If this condition is satisfied then (a,b,c)are Pythagorean triplets.

1^st case: 3² + 4² = 5². Thus this a triplet.

2^nd case: 4² + 9² ≠ 12²

3^rd case: 5² + 12² = 13² . Thus this is a triplet.

4^th case: 24^{2 +} 70² = 74². Thus this is a triplet.

5^th case: 10² + 24² ≠ 27²

6^th case: 11² + 60² = 61². Thus this is a triplet.^.