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Pythagorean Triple

Definition of Pythagorean Theorem

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 Theorem

• If a, b, c ≠ 0, and a2 + b2 = 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 Theorem

A set (5, 12, 13) is a Pythagorean triple.
52 + 122 = 25 + 144 = 169
132 = 169

Solved Example on Pythagorean Theorem

Ques: 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 integers a, b, c, which form the measures of the sides of a right-angled triangle.
Step 2: If the given measures satisfy the condition, c2 = a2 + b2, then the measures make a right triangle.
Step 3: Here, the measures 6 m, 8 m, and 10 m satisfy the condition. (102 = 62 + 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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