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Prove: If (a, a+1, a+2) is a Pythagorean triple, then a= 3

Prove: If (a, a+1, a+2) is a Pythagorean triple, then a= 3

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Answer #1

Please note that conventionally number in a Pythagorean triplet are always positive. Since, a triangle cannot have any side of negative length.

Let (a,a+1,a+2) be a Pythagorean triplet.

Then, by Pythagoras Property that is where c is the longest side, we have,

Solving this equation :

Since, a cannot be negative, a must be 3.

Therefore the triplet becomes (3,4,5).

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