In the following identify the Pythagorean triplets:(8,15,17)
Answers
Answer:
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(i) (8, 15, 17)
(ii) (18, 80, 82)
(iii) (14, 48, 51)
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.
Solution:
(i) (8, 15, 17)
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) (18, 80, 82)
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) (14, 48, 51)
The two smallest numbers are 14 and 48. The sum of their squares is:
142 + 482 = 2500, this is not equal to 512 = 2601
Hence, (14, 48, 51) is not a Pythagorean triplet.
(iv) (10, 24, 51)
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) (16, 63, 65)
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) (12, 35, 38)
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.