Suppose someone tells you that she has a triangle with sides having lengths 2.2, 4.5, and 6.7. Is this a right triangle?

You can apply the Pythagorean theorem:

a^2 + b^2 = c^2

c is the longest side of the triangle

2.2^2 + 4.2^2 = 6.7^2

4.84 + 17.64 = 44.89

22.48 = / = 44.89

That is not a right triangle