Question

Given that (5,12,13) is a Pythagorean triple, identify another example of a Pythagorean triple from the following.(1 point)
Responses

(25,60,39)
left parenthesis 25 comma 60 comma 39 right parenthesis

(10,12,13)
left parenthesis 10 comma 12 comma 13 right parenthesis

(50,120,130)
left parenthesis 50 comma 120 comma 130 right parenthesis

(15,25,39)

Answer 1

To identify another Pythagorean triple, we need to check if the sets of three numbers satisfy the Pythagorean theorem, which states that for a right triangle with legs \(a\) and \(b\) and hypotenuse \(c\), the following equation holds:

\[ a^2 + b^2 = c^2 \]

Let's evaluate each option:

1. **(25, 60, 39)**:
\[
25^2 + 60^2 = 625 + 3600 = 4225
\]
\[
39^2 = 1521
\]
Not a Pythagorean triple.

2. **(10, 12, 13)**:
\[
10^2 + 12^2 = 100 + 144 = 244
\]
\[
13^2 = 169
\]
Not a Pythagorean triple.

3. **(50, 120, 130)**:
\[
50^2 + 120^2 = 2500 + 14400 = 16900
\]
\[
130^2 = 16900
\]
This is a Pythagorean triple.

4. **(15, 25, 39)**:
\[
15^2 + 25^2 = 225 + 625 = 850
\]
\[
39^2 = 1521
\]
Not a Pythagorean triple.

The only valid Pythagorean triple from the provided options is **(50, 120, 130)**.