Which all of the following are Pythagorean triplets?

5, 12, 13

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3, 4, 5

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9, 12, 16

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10, 24, 26

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Solution

The correct options are
A
5, 12, 13

B
3, 4, 5

D
10, 24, 26

$(a) 5^{2} + 12^{2} = 25 + 144 = 169 = 13^{2} (b) 3^{2} + 4^{2} = 9 + 16 = 25 = 5^{2}$
$(c) 9^{2} + 12^{2} = 81 + 144 = 225 \neq 16^{2} Not a Pythagorean triplet$
$(d) 10^{2} + 24^{2} = 100 + 576 = 676 = 26^{2}$

Hence, (5, 12, 13) ,(3, 4, 5) and (10, 24, 26) form Pythogorean triplets.

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Similar questions

Are all of the following triplets are pythagorean?

(8, 15, 17)

(16, 63, 65)

12, 16, 20

5, 12, 13 is a Pythagorean triplet.

Q. Are the numbers

12, 5

and

13

form a Pythagorean Triplet?

Verify each of the following :

(i) $(\frac{5}{7} \times \frac{12}{13}) \times \frac{7}{18} = \frac{5}{7} \times (\frac{12}{13} \times \frac{7}{18})$
(ii) $\frac{- 13}{24} \times (\frac{- 12}{5} \times \frac{35}{36}) = (\frac{- 13}{24} \times \frac{- 12}{5}) \times \frac{35}{36}$
(iii) $(\frac{- 9}{5} \times \frac{- 10}{3}) \times \frac{21}{- 4} = \frac{- 9}{5} \times (\frac{- 10}{3} \times \frac{21}{- 4})$

Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

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Which all of the following are Pythagorean triplets?

The correct options are A 5, 12, 13 B 3, 4, 5 D 10, 24, 26 (a) 52+122=25+144=169=132(b) 32+42=9+16=25=52 (c) 92+122=81+144=225≠162 Not a Pythagorean triplet (d)102+242=100+576=676=262 Hence, (5, 12, 13) ,(3, 4, 5) and (10, 24, 26) form Pythogorean triplets.