Question

Identify, with reason, which of the following are Pythagorean triplets.

i. (24,70,74) 

ii. (10,24,27) 

iii. (11,60,61)

Answer 1

i. 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.

ii.  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. 

iii. 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.