which set of numbers reprosent a pythorgram theroy
To understand which set of numbers represent a Pythagorean triple, we need to know what a Pythagorean triple is.
A Pythagorean triple is a set of three positive integers (a, b, c) that satisfy the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Mathematically, the Pythagorean theorem can be expressed as:
a^2 + b^2 = c^2
Here are some common examples of Pythagorean triples:
- (3, 4, 5)
- (5, 12, 13)
- (8, 15, 17)
- (7, 24, 25)
To determine if a set of numbers represents a Pythagorean triple, you can check if it satisfies the Pythagorean theorem. Square each number, sum the squares of the smaller numbers, and check if it equals the square of the largest number.
For example, let's take the set of numbers (6, 8, 10). We can check if it is a Pythagorean triple by evaluating:
6^2 + 8^2 = 36 + 64 = 100
10^2 = 100
Since both sides of the equation are equal, (6, 8, 10) is indeed a Pythagorean triple.
So, any set of three positive integers (a, b, c) that satisfies the equation a^2 + b^2 = c^2 represents a Pythagorean triple.