Question

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)

Answer 1

i. Here, 5² = 25 

3² + 4² = 9 + 16 = 25 

∴ 5² = 3² + 4² 

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.

ii. Here, 12² = 144 

4² + 9² = 16 + 81 =97 

∴ 12² ≠ 4² + 9²

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.

iii. Here, 13² = 169 

5² + 12² = 25 + 144 = 169 

∴ 13² = 5² + 12² 

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.

iv. Here, 74² = 5476 

24² + 70² = 576 + 4900 = 5476 

∴ 74² = 24² + 70² 

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.

v. Here, 27² = 729 

10² + 24² = 100 + 576 = 676 

∴ 27² ≠ 10² + 24² 

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.

vi. Here, 61² = 3721 

11² + 60² = 121 + 3600 = 3721 

∴ 61² = 11² + 60² 

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.