Which set represents a Pythagorean triple
A Pythagorean triple is a set of three positive integers (a, b, and c) that satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
To determine if a set represents a Pythagorean triple, you can check if the given numbers satisfy the Pythagorean theorem.
The most common Pythagorean triple is (3, 4, 5). Let's check if this set satisfies the Pythagorean theorem:
3^2 + 4^2 = 5^2
9 + 16 = 25
25 = 25
Since the equation holds true, (3, 4, 5) is indeed a Pythagorean triple.
Other examples of Pythagorean triples include:
- (5, 12, 13)
- (8, 15, 17)
- (7, 24, 25)
To determine if a given set of three numbers represents a Pythagorean triple, you can simply check if a^2 + b^2 = c^2. If the equation holds true, then it is a Pythagorean triple.