Find a Pythagorean triplet whose one member is 22.

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22, 121 and 122

22, 122 and 124

22, 120 and 122

22, 120 and 124

answer is B.

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Detailed Solution

We know that the Pythagorean triplets can be found by using the general form 2m, m² − 1, m² + 1, where m is a natural number greater than 1.

If m² − 1 = 22

⇒ m² = 22 + 1 = 23

Then, the value of m will not be an integer.

If m² + 1 = 22

⇒ m² = 22 − 1 = 21

Then, the value of m will not be an integer.

Therefore, let 2m = 22

⇒ m = 11, which is a natural number greater than 1

∴ m² − 1 = 11² − 1 = 121 − 1 = 120,

m² + 1 = 11² + 1 = 121 + 1 = 122

Therefore, the required Pythagorean triplet is 22, 120 and 122.

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