Pythagorean Triplets

Table of Contents

• Pythagoras Theorem
• Pythagorean Triplets
• Summary
• What’s Next?

In this segment, we will learn about the Pythagorean triplets.

What is the Pythagoras theorem?

The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.

So, in a right-angled triangle if a and b are the perpendicular sides and c is the hypotenuse, then,

?² = ?² + ?².

For example, if a= 3 units and b=4 units are sides of a right-angled triangle, then the hypotenuse c is given by

?² = ?² + ?²

∴ ?² = 3² + 4²

∴ ?² = 9 + 16

∴ ?² = 25

∴ ? = √25

∴ c= 5

Thus, the hypotenuse is 5 units.

What are Pythagorean triplets?

For any natural number m > 1, if (2?)² + (?² − 1)² = (?² + 1)², then 2?, ?² − 1 ??? ?² + 1form a pythagorean triplet.

For example,