Question

how to prove (3,4,5) is pythagorian triplets?

Answer 1

Find out the largest side, in this case it is 5.
Now check that whether the sum of squares of the other two sides is equal to the square of the largest side. If it is, then it is a Pythagorean triplet.
${3}^{2} + {4}^{2} = 9 + 16 = 25 = {5}^{2}$
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Answer 2

the triplets above such as 3,4,5 represent the ratios of side lengths that satisfy the pythagorean theorem.you can use the above triplets to make another triplet by just multyplying it

(3,4,5) ×2 = 8,6,10 and 8,6,10 is also a pythagorean triplet(5,12,13) ×2 = 10,24,26 and 10,24,26 is also a pythagorean triplet