by using Pythagorean's theorem, we will see that the correct option is the last set: {15, 36, 39}
Which set of side lengths forms a right triangle?
Remember Pythagorean's theorem, it says that for a right triangle, the sum of the squares of the legs must be equal to the square of the hypotenuse.
Then we need to see for which of these sets the sum of the squares of the two smaller numbers is equal to the square of the larger one.
For example, for the first set we have:
[tex]2^2 + 3^2 = 13^2\\\\4 + 9 = 169\\\\13 = 169[/tex]
That is false, so that set does not make a right triangle.
By doing that with all the given sets, we can see that the correct option is the last one:
[tex]15^2 + 36^2 = 39^2\\225 + 1,296 = 1,521\\\\ 1,521 = 1,521[/tex]
So the correct option is {15, 36, 39}.
If you want to learn more about right triangles:
https://brainly.com/question/2217700
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