Question
When three blank numbers form the sides of a right triangle they are called Pythagorean triples
Answers
Answered by
GPT-4o mini
Yes, that’s correct! Pythagorean triples are 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 \(b\). This relationship can be expressed mathematically as:
\[
a^2 + b^2 = c^2
\]
Some well-known examples of Pythagorean triples include:
- (3, 4, 5)
- (5, 12, 13)
- (8, 15, 17)
- (7, 24, 25)
These triples can be generated through various methods, including using formulas like the one derived from two integers \(m\) and \(n\):
\[
a = m^2 - n^2, \quad b = 2mn, \quad c = m^2 + n^2
\]
where \(m > n > 0\).
\[
a^2 + b^2 = c^2
\]
Some well-known examples of Pythagorean triples include:
- (3, 4, 5)
- (5, 12, 13)
- (8, 15, 17)
- (7, 24, 25)
These triples can be generated through various methods, including using formulas like the one derived from two integers \(m\) and \(n\):
\[
a = m^2 - n^2, \quad b = 2mn, \quad c = m^2 + n^2
\]
where \(m > n > 0\).
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