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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)

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+1 vote
i. (3,5,4)
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. (4,9,12)
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. (5,12,13)
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. (24,70,74)
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. (10,24,27)
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. (11,60,61)
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.

by Expert (10.7k points)