Question

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

Answer 1

(i) The given set of numbers is (3, 4, 5).

The biggest number among the given set is 5.

$5^2=25;4^2=16;3^2=9$

Now, 16 + 9 = 25

$\therefore 4^2+3^2=5^2$

Thus, (3, 4, 5) forms a Pythagorean triplet

(ii) The given set of numbers is (9, 40, 41).

The biggest number among the given set is 41.

$9^2=81;{40}^2=1600;{41}^2=1681$

Now, 81 + 1600 = 1681

$\therefore 9^2+{40}^2={41}^2$

Thus, (9, 40, 41) forms a Pythagorean triplet.

(iii) The given set of numbers is (4, 7, 8).

The biggest number among the given set is 8.

$8^2=64;7^2=49;4^2=16$

Now, 16 + 49 = 65 $\ne$ 64

$\therefore 4^2+7^2\ne 8^2$

Thus, (4, 7, 8) does not form a Pythagorean triplet.