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)

i. (3,5,4)

ii. (4,9,12)

iii. (5,12,13)

iv. (24,70,74)

v. (10,24,27)

vi. (11,60,61)

Here,

5^{2} = 25

3^{2} + 4^{2} = 9 + 16 = 25

∴ 5^{2} = 3^{2} + 4^{2}

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

∴ (3,5,4) is a Pythagorean triplet.

5

3

∴ 5

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

∴ (3,5,4) is a Pythagorean triplet.

Here,

12^{2} = 144

4^{2} + 9^{2}= 16 + 81 =97

∴ 12^{2} ≠ 4^{2} + 9^{2}

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

∴ (4,9,12) is not a Pythagorean triplet.

12

4

∴ 12

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

∴ (4,9,12) is not a Pythagorean triplet.

Here,

13^{2} = 169

5^{2} + 12^{2} = 25 + 144 = 169

∴ 13^{2} = 5^{2} + 12^{2}

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

∴ (5,12,13) is a Pythagorean triplet.

13

5

∴ 13

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

∴ (5,12,13) is a Pythagorean triplet.

Here,

74^{2} = 5476

24^{2} + 70^{2} = 576 + 4900 = 5476

∴ 74^{2} = 24^{2} + 70^{2}

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

∴ (24, 70,74) is a Pythagorean triplet.

74

24

∴ 74

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

∴ (24, 70,74) is a Pythagorean triplet.

Here,

27^{2} = 729

10^{2} + 24^{2} = 100 + 576 = 676

∴ 27^{2} ≠ 10^{2} + 24^{2}

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

∴ (10,24,27) is not a Pythagorean triplet.

27

10

∴ 27

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

∴ (10,24,27) is not a Pythagorean triplet.

Here,

61^{2} = 3721

11^{2} + 60^{2} = 121 + 3600 = 3721

∴ 61^{2} = 11^{2} + 60^{2}

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

∴ (11,60,61) is a Pythagorean triplet.

61

11

∴ 61

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

∴ (11,60,61) is a Pythagorean triplet.