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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 (15,25,39) left parenthesis 15 comma 25 comma 39 right parenthesis (50,120,130)

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To verify which of the given triples is another Pythagorean triple, we can use the Pythagorean theorem, which states that in a right triangle with sides \( a \) and \( b \), and hypotenuse \( c \), the following equation holds:

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

Let's check each of the options:

  1. (25, 60, 39)

    • \( 25^2 + 60^2 = 625 + 3600 = 4225 \)
    • \( 39^2 = 1521 \)
    • Since \( 4225 \neq 1521 \), this is not a Pythagorean triple.

  2. (10, 12, 13)

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

  3. (15, 25, 39)

    • \( 15^2 + 25^2 = 225 + 625 = 850 \)
    • \( 39^2 = 1521 \)
    • Since \( 850 \neq 1521 \), this is not a Pythagorean triple.

  4. (50, 120, 130)

    • \( 50^2 + 120^2 = 2500 + 14400 = 16900 \)
    • \( 130^2 = 16900 \)
    • Since \( 16900 = 16900 \), this is a valid Pythagorean triple.

The correct answer is (50, 120, 130).