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

Question

Responses

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

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

(15,25,39)
left parenthesis 15 comma 25 comma 39 right parenthesis

(10,12,13)

Answer 1

To identify a Pythagorean triple, we need to find a set of three integers \( (a, b, c) \) such that \( a^2 + b^2 = c^2 \).

Let's check each option given:

1. (25, 60, 39):

   • \( 25^2 + 60^2 = 625 + 3600 = 4225 \)
   • \( 39^2 = 1521 \)
   • Not a Pythagorean triple.

2. (50, 120, 130):

   • \( 50^2 + 120^2 = 2500 + 14400 = 16900 \)
   • \( 130^2 = 16900 \)
   • This is a Pythagorean triple.

3. (15, 25, 39):

   • \( 15^2 + 25^2 = 225 + 625 = 850 \)
   • \( 39^2 = 1521 \)
   • Not a Pythagorean triple.

4. (10, 12, 13):

   • \( 10^2 + 12^2 = 100 + 144 = 244 \)
   • \( 13^2 = 169 \)
   • Not a Pythagorean triple.

The only option that forms a Pythagorean triple is (50, 120, 130).