Question

Given that (5,12,13) is a Pythagorean triple, identify another example of a Pythagorean triple from the following.(1 point) Responses (10,12,13) left parenthesis 10 comma 12 comma 13 right parenthesis (25,60,39) left parenthesis 25 comma 60 comma 39 right parenthesis (15,25,39) left parenthesis 15 comma 25 comma 39 right parenthesis (50,120,130)

Answer 1

To determine which of the provided options represents a Pythagorean triple, we need to check each set of numbers (a, b, c) to see if they satisfy the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(c\) is the largest number.

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

2. **For (25, 60, 39)**:
\[
25^2 + 39^2 = 625 + 1521 = 2146
\]
\[
60^2 = 3600
\]
(Not a Pythagorean triple)

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

4. **For (50, 120, 130)**:
\[
50^2 + 120^2 = 2500 + 14400 = 16900
\]
\[
130^2 = 16900
\]
(This satisfies the Pythagorean theorem)

So, the Pythagorean triple from the given options is **(50, 120, 130)**.