Pythagorean Triples Formula

Pythogorean triplets formula is used to generate a triple which will follow the Pythagorean theorem. When the given sides of a triangle are there in the form of Pythagoras theorem, then the same right-angled triangle is said to be Pythagorean triples. To label a triangle as Pythagorean triples they should satisfy the condition of Pythagoras theorem. The triples are commonly written as (a,b,c)

Where a and b are the two sides and the longest side, the hypotenuse is written as (c). The smallest known Pythagorean triples are  (2,3 and 5)

Pythagorean Triples Formula

Pythagorean Triples Formula

The Pythagorean Theorem Formula is,

c2 = a2 + b2

Formula for Pythagorean Triples

To find the pyhthogorean triples, the following formual is used. If a, b are two sides of the triangle and c is the hypotenuse, then, a, b, and c can be found out using this-

  • a = k. (m2-n2),
  • b = k.(2mn), and
  • c = k. (m2+n2)

Notes:

(i) m, n and k are any two positive integers

(ii) m > n

(iii) m and n are coprime and both should not be odd numbers

Also Check: Pythagorean Triples Calculator

Solved Examples

Question 1: Check if (7, 24, 25) are Pythagorean triples?

Solution: Given, Pythagorean triples = (7, 24, 25) a = 7 b = 24 c = 25 The Pythagorean triples formula is, c2 = a2 + b2 LHS: c2 = 252 = 625 RHS: a2 + b2 = 72 + 242 = 49 + 576 = 625 LHS = RHS So (7, 24, 25) is a Pythagorean triples.

Common Pythagorean Triples:

Here is the list of the most commonly used Pythagorean triples: Pythogorean Triples


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