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Which of the following is Pythagorean triplet?

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3 ,4 ,5

5, 12, 13

7, 24, 25

All of these

answer is D.

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Detailed Solution

Given triplets in options are (3,4,5), (5,12,13) and (7,24,25).
If

a^{2} + b^{2} = c^{2}

, then a, b and c are called Pythagorean triplet.
Checking first triplet.

3^{2} + 4^{2} = 9 + 16

{\Rightarrow 3}^{2} + 4^{2} = 25

{\Rightarrow 3}^{2} + 4^{2} = 5^{2}

Thus, (3,4,5) is a Pythagorean triplet.
Checking second triplet.

5^{2} + 12^{2} = 25 + 144

{\Rightarrow 5}^{2} + 12^{2} = 169

{\Rightarrow 5}^{2} + 12^{2} = 13^{2}

Thus, (5,12,13) is a Pythagorean triplet.
Checking third triplet.

7^{2} + 24^{2} = 49 + 576

{\Rightarrow 7}^{2} + 24^{2} = 625

{\Rightarrow 7}^{2} + 24^{2} = 25^{2}

Thus, (7,24,25) is a Pythagorean triplet.
Hence, all the given triplets are Pythagorean triplets.
Therefore, option (4) is correct.

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