Is the ABC triangle, in which AB = 4, BC = 5, AC = 6, is it rectangular?

Suppose that triangle ABC is rectangular, then its largest side is the hypotenuse of triangle ABC.

Then, according to the Pythagorean theorem, the square of the hypotenuse should be equal to the sum of the squares of the legs.

AC ^ 2 = 6 ^ 2 = 36.

AB ^ 2 + BC ^ 2 = 4 ^ 2 + 5 ^ 2 = 16 + 25 = 41.

36 ≠ 41, therefore, triangle ABC is not right-angled.

Answer: It is not.