which of the following are Pythagoras triplets 1.(3,5,4) 2.(4,9,12) 3.(5,12,13)4.(24,70,74) 5.(10,24,27)6.(11,60,64)
Answers
Answer:
In the triplet (3, 5, 4),
32 = 9, 52 = 25, 42 = 16 and 9 + 16 = 25
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) In the triplet (4, 9, 12),
42 = 16, 92 = 81, 122 = 144 and 16 + 81 = 97 ≠ 144
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) In the triplet (5, 12, 13),
52 = 25, 122 = 144, 132 = 169 and 25 + 144 = 169
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) In the triplet (24, 70, 74),
242 = 576, 702 = 4900, 742 = 5476 and 576 + 4900 = 5476
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) In the triplet (10, 24, 27),
102 = 100, 242 = 576, 272 = 729 and 100 + 576 = 676 ≠ 729
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) In the triplet (11, 60, 61),
112 = 121, 602 = 3600, 612 = 3721 and 121 + 3600 = 3721
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.