**Definition of Pythagorean Triple**

- A set of three non-zero numbers whose sum of the squares of two numbers is equal to the square of the third number.

**More about Pythagorean Triple**

- If
*a*,*b*,*c*≠ 0, and*a*^{2}+*b*^{2}=*c*^{2}, then (*a*,*b*,*c*) is called a Pythagorean triple. - Measures of a Pythagorean triple make a right triangle.
- If
*a*,*b*, and*c*form a Pythagorean triple, then for any positive number*n*,*na*,*nb*, and*nc*also form a Pythagorean triple i.e. if 3, 4, and 5 form a Pythagorean triple, then 3(3, 4, 5) i.e. 9, 12, and 15 also form a Pythagorean triple.

**Example of Pythagorean Triple**

- A set (5, 12, 13) is a Pythagorean triple.

5^{2}+ 12^{2}= 25 + 144 = 169

13^{2}= 169

**Solved Example on Pythagorean Triple**

Which of the following is a Pythagorean triple?

Choices:

A. 6 m, 8 m, 10 m

B. 5 m, 7 m, 9 m

C. 6 m, 7 m, 8 m

D. 5 m, 6 m, 7 m

Correct Answer: A

Solution:

Step 1:Pythagorean triples are a set of three integersa,b,c, which form the measures of the sides of a right-angled triangle.

Step 2:If the given measures satisfy the condition,c^{2}=a^{2}+b, then the measures make a right triangle.^{2}

Step 3:Here, the measures 6 m, 8 m, and 10 m satisfy the condition. (10^{2}= 6^{2}+ 8^{2}⇒ 100 = 36 + 64 = 100)

Step 4:Thus, the measures 6 m, 8 m, and 10 m make a right triangle and thus it is a Pythagorean triple.

**Related Terms for Pythagorean Triple**

- Pythagorean Theorem
- Right Triangle
- Square Number