#### Question

Some question and their alternative answer are given. Select the correct alternative.

Out of the following which is the Pythagorean triplet?

(1, 5, 10)

(3, 4, 5)

(2, 2, 2)

(5, 5, 2)

#### Solution

(1) (A) In the triplet (1, 5, 10),

1^{2} = 1, 5^{2} = 25, 10^{2} = 100 and 1 + 25 = 26 ≠ 100

The square of the largest number is not equal to the sum of the squares of the other two numbers.

∴ (1, 5, 10) is not a pythagorean triplet.

(B) In the triplet (3, 4, 5),

3^{2} = 9, 4^{2} = 16, 5^{2} = 25 and 9 + 16 = 25

The square of the largest number is equal to the sum of the squares of the other two numbers.

∴ (3, 4, 5) is a pythagorean triplet.

(C) In the triplet (2, 2, 2),

2^{2} = 4, 2^{2} = 4, 2^{2} = 4 and 4 + 4 = 8 ≠ 4

The square of the largest number is not equal to the sum of the squares of the other two numbers.

∴ (2, 2, 2) is not a pythagorean triplet.

(D) In the triplet (5, 5, 2),

2^{2} = 4, 5^{2} = 25, 5^{2} = 25 and 4 + 25 = 29 ≠ 25

The square of the largest number is not equal to the sum of the squares of the other two numbers.

∴ (5, 5, 2) is not a pythagorean triplet.

Hence, the correct option is (3, 4, 5).