What are the Pythagorean triplets, whose smallest number is 18?

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18, 82, 84

18, 82, 86

18, 80, 82

18, 80, 84

answer is C.

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Detailed Solution

It is required to find the Pythagorean triplets, whose smallest number is 18.
For any natural number m > 1,

2 m 2 + m 2 − 1 2 = m 2 + 1 2

2 m, (m 2 − 1), (m 2 + 1)

form a Pythagorean triplet.
The smallest number = 18,

∴ 2m = 18 ⇒ m = 9

Find the other numbers,

\Rightarrow m^{2} - 1 = 9^{2} - 1

\Rightarrow 81 - 1 = 80

\Rightarrow m^{2} + 1 = 9^{2} + 1

\Rightarrow 81 + 1 = 82

The Pythagorean triplets are therefore 18, 80, and 82, with 18 being the smallest number.
Therefore, option 3 is correct.

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