Question

given that (5,12,13) is a Pythagorean triple, identify another example of a Pythagorean triple from the following.
A. (15,25,39)
B. (50,120,130)
C. (25, 60, 39)
D. (10,12,13)

Answer 1

A Pythagorean triple consists of three positive integers \(a\), \(b\), and \(c\) such that \(a^2 + b^2 = c^2\).

Let's evaluate each option:

A. (15, 25, 39)
\[
15^2 + 25^2 = 225 + 625 = 850 \quad \text{and} \quad 39^2 = 1521
\]
Not a Pythagorean triple.

B. (50, 120, 130)
\[
50^2 + 120^2 = 2500 + 14400 = 16900 \quad \text{and} \quad 130^2 = 16900
\]
This is a Pythagorean triple.

C. (25, 60, 39)
\[
25^2 + 60^2 = 625 + 3600 = 4225 \quad \text{and} \quad 39^2 = 1521
\]
Not a Pythagorean triple.

D. (10, 12, 13)
\[
10^2 + 12^2 = 100 + 144 = 244 \quad \text{and} \quad 13^2 = 169
\]
Not a Pythagorean triple.

From the options given, the only valid Pythagorean triple is:

**B. (50, 120, 130)**