Question

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

a. (10,12,13)
b. (50,120,130)
c. (25,60,39)
d. (15,25,39)

Answer 1

To determine which of the given options is a Pythagorean triple, we can use the Pythagorean theorem, which states that for a set of integers \(a\), \(b\), and \(c\) (where \(c\) is the longest side), the equation \(a^2 + b^2 = c^2\) should hold true.

Now let's evaluate each option:

a. \( (10, 12, 13) \)
\[
10^2 + 12^2 = 100 + 144 = 244
\]
\[
13^2 = 169
\]
\(244 \neq 169\) so this is not a Pythagorean triple.

b. \( (50, 120, 130) \)
\[
50^2 + 120^2 = 2500 + 14400 = 16900
\]
\[
130^2 = 16900
\]
\(16900 = 16900\) so this is a Pythagorean triple.

c. \( (25, 60, 39) \)
\[
25^2 + 60^2 = 625 + 3600 = 4225
\]
\[
39^2 = 1521
\]
\(4225 \neq 1521\) so this is not a Pythagorean triple.

d. \( (15, 25, 39) \)
\[
15^2 + 25^2 = 225 + 625 = 850
\]
\[
39^2 = 1521
\]
\(850 \neq 1521\) so this is not a Pythagorean triple.

From the evaluations, the only example of a Pythagorean triple from the provided options is:

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