Practice Questions on Pythagorean Triples

What are Pythagorean Triplets?

Pythagorean triples are use to find the three positive integers that satisfy the Pythagoras theorem. Generally, these three terms can be written in the form (a, b, c), and form a right-angle triangle with c as its hypotenuse and a and b as its base and height. The triangle formed by these terms is known as the Pythagorean triangle....

Pythagorean Triples Examples

There are infinitely many possible Pythagorean triples as we can choose any two numbers for base and perpendicular and we can find hypotenuse using the Pythagoras theorem. For example, let’s say the perpendicular of the triangle is 4 units, and the base is 3 units, then the hypotenuse will be 5 using the Pythagoras theorem. This is further explained in the image added below....

Pythagorean Triples Formula

Pythagorean Triples Formula is derived from the right-angled triangle. The sides of the right-angle triangle arranged in increasing order as triples are Pythagorean triples. If two values out of three in a Pythagorean triple is given, the third can be obtained from the Pythagoras theorem which is also known as Pythagorean Triplets Formula....

Pythagorean Triples Formula Proof

Proof of the Pythagorean triplets Formula or Pythagoras theorem can be done in many ways. There are well over 371 proofs for this formula. Here we are using one of the many geometric methods. In this method, we use the figure as follows:...

How to Form Pythagorean Triples?

Pythagorean triples are the positive integers and there are two cases for the number that can help us generate Pythagorean triples. The numbers can either be odd or even. The cases mentioned above can be explained in detail, as follows:...

How to Generate Pythagorean Triples?

Other than the method illustrated above in this article, there is another way to generate Pythagorean Triples. In order to generate Pythagorean triples, we can assume the sides of the right-angled triangle are a, b, and c and define these sides in terms of two integral values m and n, such that,...

Pythagorean Triples List

Below is the list of some of the Pythagorean triplets where the value of c (the hypotenuse of the triangle) is greater than 100:...

Types of Pythagorean Triples

Pythagorean Triples can further be classified into two types namely:...

Properties of Pythagorean Triples

For a right-angled triangle with base m, height n, and hypotenuse p, Pythagorean triples have the following properties:...

Triangular Numbers

We know that a triangular number is a number that can be arranged to form a triangle using the number of tiles as the number itself. As it is evident that the difference between two successive squares is successive odd numbers which suggests that every square is the sum of two successive triangular numbers....

Pythagorean Triples Solved Examples

Example 1: Find Pythagorean triples if m = 8....

Practice Questions on Pythagorean Triples

Question 1: Find the Pythogorean triples of 21....

Summary – Pythagorean Triples

The article discusses Pythagorean triples, which are sets of three integers (a, b, c) that satisfy the equation a2 + b2 = c2 and represent the sides of a right triangle. It explains how these triples can be generated using formulas based on whether the initial integer (m) is odd or even, offering specific examples such as (3, 4, 5) and (5, 12, 13). The article also covers methods for creating these triples by manipulating two co-prime integers, m and n, ensuring that m is greater than n, to satisfy the Pythagorean theorem. This exploration of Pythagorean triples illustrates their fundamental role in geometric and algebraic concepts, emphasizing their practical and theoretical significance in mathematics....

FAQs on Pythagorean Triples

What are the Pythagorean Triples?...