Which of the following triplets are pythagorean?

Solution:

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.