Question

Write two Pythagorean triplets each having one of the numbers as 5.

Answer 1

Given: We know that for any natural number greater than 1, (2m, m² – 1, m² + 1) is a the Pythagorean triplet.

So if one number is m² + 1 then other two number are m² – 1 and 2m.

i.e. m² + 1 = 5  ...(Given)

⇒ m² = 4

⇒ m = 2

Then m² – 1

= 2² – 1

= 4 – 1

= 3

And 2m = 2(2) = 4

Hence, Pythagorean triplet is 3, 4 and 5

Similarly another triplet is:

• We need a² + b² = c²
• Let's try b = 12 and solve for c:
  • 5² + 12² = 25 + 144 = 169
  • c² = 169
  • c = `sqrt(169)` = 13

Thus, the triplet is (5, 12, 13).

Hence, 3, 4, 5 and 5, 12, 13 are two Pythagorean triplet.