Question

Find the Pythagorean triplets from among the following sets of numbers.
(i) 3, 4, 5
(ii) 2, 4, 5
(iii) 4, 5, 6
(iv) 2, 6, 7
(v) 9, 40, 41
(vi) 4, 7, 8

Answer 1

It is known that, if in a triplet of natural numbers, the square of the biggest number is equal to sum of the squares of the other two numbers, then the three numbers form a Pythgorean triplet.

(i) The given set of numbers is (3, 4, 5).
The biggest number among the given set is 5.
5² = 25; 4² = 16; 3² = 9
Now, 16 + 9 = 25
∴ 4² + 3² = 5²
Thus, (3, 4, 5) forms a Pythagorean triplet.

(ii) The given set of numbers is (2, 4, 5).
The biggest number among the given set is 5.
5² = 25; 4² = 16; 2² = 4
Now, 16 + 4 = 20 ≠ 25
∴ 4² + 2² ≠ 5²
Thus, (2, 4, 5) does not form a Pythagorean triplet.

(iii) The given set of numbers is (4, 5, 6).
The biggest number among the given set is 6.
6² = 36; 5² = 25; 4² = 16
Now, 25 + 16 = 41 ≠ 36
∴ 5² + 4² ≠ 6²
Thus, (4, 5, 6) does not form a Pythagorean triplet.

(iv) The given set of numbers is (2, 6, 7).
The biggest number among the given set is 7.
7² = 49; 6² = 36; 2² = 4
Now, 4 + 36 = 40 ≠ 49
∴ 2² + 6² ≠ 7²
Thus, (2, 6, 7) does not form a Pythagorean triplet.

(v) The given set of numbers is (9, 40, 41).
The biggest number among the given set is 41.
9² = 81; 40² = 1600; 41² = 1681
Now, 81 + 1600 = 1681
∴ 9² + 40² = 41²
Thus, (9, 40, 41) forms a Pythagorean triplet.

(vi) The given set of numbers is (4, 7, 8).
The biggest number among the given set is 8.
8² = 64; 7² = 49; 4² = 16
Now, 16 + 49 = 65 ≠ 64
∴ 4² + 7² ≠ 8²
Thus, (4, 7, 8) does not form a Pythagorean triplet.