Can someone please help me with this Geometry question?

Question

Tell whether the given side lengths form a right triangle.

5, 7, 10

I got: Yes

Here’s my reason:

5 + 7 > 10

5 + 10 > 7

7 + 10 > 5

Answer 1

You applied the Triangle Inequality Theorem, which proves you can make a triangle with sides 5, 7, and 10; but it does not prove it's a right triangle. To do that, you apply the Pythagorean Theorem. If 5² + 7² = 10², it's a right triangle. Otherwise it isn't.