Given that (5,12,13)

Question

is a Pythagorean triple, which of the following is also a Pythagorean triple?(1 point)
Responses

(4,11,12)
left parenthesis 4 comma 11 comma 12 right parenthesis

(10,24,25)
left parenthesis 10 comma 24 comma 25 right parenthesis

(15,36,39)
left parenthesis 15 comma 36 comma 39 right parenthesis

(7,14,15)

Answer 1

To determine which of the given options is a Pythagorean triple, we need to check if the sum of the squares of the two smaller numbers equals the square of the largest number in each set.

1. For (4, 11, 12): \(4^2 + 11^2 = 16 + 121 = 137\) \(12^2 = 144\) \(137 ≠ 144\) → Not a Pythagorean triple.

2. For (10, 24, 25): \(10^2 + 24^2 = 100 + 576 = 676\) \(25^2 = 625\) \(676 ≠ 625\) → Not a Pythagorean triple.

3. For (15, 36, 39): \(15^2 + 36^2 = 225 + 1296 = 1521\) \(39^2 = 1521\) \(1521 = 1521\) → This is a Pythagorean triple.

4. For (7, 14, 15): \(7^2 + 14^2 = 49 + 196 = 245\) \(15^2 = 225\) \(245 ≠ 225\) → Not a Pythagorean triple.

Out of the given options, (15, 36, 39) is a Pythagorean triple.