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Pythagorean Triples Calculator

Free Pythagorean Triples Calculator is available here to give the instant results i.e does your numbers satisfy the Pythagorean theorem rule. Our handy calculator tool takes input as lengths of three sides of triangle and produces output as whether it forms a right angled triangle or not.

Pythagorean Triples Calculator: If you want to check either the given numbers make a right angled triangle or not, then use this online calculator tool. You must enter three sides lengths of triangle in the input fields and press on calculate button to avail the results as early as possible. Furthermore, we even added the step by step process to get the whether the numbers form a 90 degree angle using Pythagorean triples theorem with solved examples in the following sections.

Steps to Find Triangle Side Using Pythagorean Triples Theorem

Have a look at the manual procedure in the below sections. Follow these guidelines to get the right angled triangle sides with the Pythagorean Triples Theorem.

  • Get the length of three sides of the triangle.
  • We already know that, the sides of right angled triangle are Perpendicular side (a), Base Side (b), Hypotenuse Side (c).
  • As per the Pythagorean Triples Theorem the sum of squares of perpendicular side and base side is equal to the square of hypotenuse side.
  • The mathematical representation of theorem is c2 = a2 + b2
  • Substitute the values in the formula and perform math operation.
  • If the result obtained on the left hand side is equal to the right hand side, then it forms a right angled triangle.


Question: Does 9, 12 and 15 make a right triangle?


Given that,Base side length (a) = 9 cm

Perpendicular side length (b) = 12 cm

Hypotenuse side length (c) = 15

According to the Pythagorean Triples Theorem

c2 = a2 + b2

Substitute the given values in the Pythagorean theorem to know whether it forms a right angles triangle or not.

152 = 92 + 122

225 = 81 + 144

225 = 225

Therefore 9, 12, 15 forms a right angled triangle.

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Pythagorean Triples Calculator

FAQ's on Pythagorean Triples Calculator

1. Does Pythagorean theorem work on all triangles?

Pythagorean theorem works only on right angled triangles.

2. What are the 5 most common Pythagorean triples?

The five most common Pythagorean triples are (3, 4, 5), (5, 12, 13), (7, 24, 26), (9, 40, 41), (11, 60, 61).

3. What is the Pythagorean triplet of 14?

Let us take 2n = 14

n = 7

n2 - 1 = 72 - 1

= 49 - 1 = 48

n2 + 1 = 72 + 1

= 49 + 1 = 50

The required triplet is (14, 48, 50)

4. What is the hypotenuse of triangle when base is 5 cm and perpendicular side is 12 cm?

Base side length (a) = 5 cm

Perpendicular side length (b) = 12 cm

Hypotenuse side length (c) = ?

c2 = a2 + b2

= 52 + 122

= 25 + 144

= 169

c = √169

= 13

Therefore, Hypotenuse c = 13.