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

Question

(1 point)
O (10,12, 13)
О (15,25, 39)
• (50, 120, 130)
О (25, 60,39)

Answer 1

To identify another Pythagorean triple, we need to check each of the given sets of numbers to see if they satisfy the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) equals the square of the longest side (hypotenuse).

Let's check the options one by one:

1. (10, 12, 13):

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

2. (15, 25, 39):

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

3. (50, 120, 130):

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

4. (25, 60, 39):

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

Therefore, the only set that represents a Pythagorean triple is (50, 120, 130).