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Write three sets of Pythagorean triplets such that each set has numbers less than 30.

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#### Solution

The three sets of Pythagorean triplets such that each set has numbers less than 30 are 3, 4 and 5; 6, 8 and 10; 5, 12 and 13

Proof:

In 3, 4 and 5

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

⇒ 9 + 16 = 25

⇒ 25 = 25

In 6, 8 and 10

6^{2} + 8^{2} = 10^{2}

⇒ 36 + 64 = 100

⇒ 100 = 100

In 5, 12, and 13

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

⇒ 25 + 144 = 169

⇒ 169 = 169

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