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

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

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

(25,60,39)

1 answer

To identify another example of a Pythagorean triple, we need to check which of the given sets of numbers satisfy the equation \( a^2 + b^2 = c^2 \), where \( c \) is the largest number.

  1. (10, 12, 13): \[ 10^2 + 12^2 = 100 + 144 = 244 \quad \text{and} \quad 13^2 = 169 \quad \text{(not a Pythagorean triple)} \]

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

  3. (50, 120, 130): \[ 50^2 + 120^2 = 2500 + 14400 = 16900 \quad \text{and} \quad 130^2 = 16900 \quad \text{(is a Pythagorean triple)} \]

  4. (25, 60, 39): \[ 25^2 + 60^2 = 625 + 3600 = 4225 \quad \text{and} \quad 39^2 = 1521 \quad \text{(not a Pythagorean triple)} \]

From the evaluations, the only example of a Pythagorean triple from the given options is (50, 120, 130).