Pythagorean Triple
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Definition of Pythagorean Theorem

A set of three nonzero numbers whose sum of the squares of two numbers is equal to the square of the third number.
More About Pythagorean Theorem
 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.
Video Examples: Pythagorean triples
Example of Pythagorean Theorem

A set (5, 12, 13) is a Pythagorean triple.
5^{2} + 12^{2} = 25 + 144 = 169
13^{2} = 169
Solved Example on Pythagorean Theorem
Ques: Which of the following is a Pythagorean triple?
Choices:
A. 6 m, 8 m, 10 mB. 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 integers a, b, c, which form the measures of the sides of a rightangled triangle.
Step 2: If the given measures satisfy the condition, c^{2} = a^{2} + b^{2}, then the measures make a right triangle.
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.
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