Question

>> The Converse of the Pythagorean Theorem states that if a triangle has side lengths a, b, and c with a² + b² = c², then the triangle is a right triangle.
Which triangle is a right triangle?
6
12
13
13
12
5

Answer 1

Check each triple using a² + b² = c² (with c the longest side).

For 6, 12, 13: 6² + 12² = 36 + 144 = 180, but 13² = 169 ⇒ not right.

For 13, 12, 5 (i.e. 5, 12, 13): 5² + 12² = 25 + 144 = 169 = 13² ⇒ this is a right triangle.

So the triangle with sides 5, 12, 13 is right.