Question

Which of the following triplets are pythagorean?
(i) (8, 15, 17)
(ii) (18, 80, 82)
(iii) (14, 48, 51)
(iv) (10, 24, 26)
(v) (16, 63, 65)
(vi) (12, 35, 38)

Answer 1

Only (i), (ii), (iv) and (v) are Pythagorean triplets.
A triplet (a, b, c) is called Pythagorean if the sum of the squares of the two smallest numbers is equal to the square of the biggest number.

(i) The two smallest numbers are 8 and 15. The sum of their squares is:
8² + 15² = 289 = 17²
Hence, (8, 15, 17) is a Pythagorean triplet.

(ii) The two smallest numbers are 18 and 80. The sum of their squares is:
18² + 80² = 6724 = 82²
Hence, (18, 80, 82) is a Pythagorean triplet.

(iii) The two smallest numbers are 14 and 48. The sum of their squares is:
14² + 48² = 2500, which is not equal to 51² = 2601
Hence, (14, 48, 51) is not a Pythagorean triplet.

(iv) The two smallest numbers are 10 and 24. The sum of their squares is:
10² + 24² = 676 = 26²
Hence, (10, 24, 26) is a Pythagorean triplet.

(v) The two smallest numbers are 16 and 63. The sum of their squares is:
16² + 63² = 4225 = 65²
Hence, (16, 63, 65) is a Pythagorean triplet.

(vi) The two smallest numbers are 12 and 35. The sum of their squares is:
12² + 35² = 1369, which is not equal to 38² = 1444
Hence, (12, 35, 38) is not a Pythagorean triplet.