The sides of the triangle are 9 cm, 12 cm and 14 cm. Is this triangle right-angled?

In a right-angled triangle, the hypotenuse squared is equal to the sum of the squares of its legs.

In order to determine whether this triangle is rectangular, it is necessary to calculate whether the conditions of the Pythagorean theorem are fulfilled:

AB ^ 2 = BC ^ 2 + AC ^ 2.

Let’s assume that AB = 14 cm; BC = 12 cm; AC = 9 cm.

AB ^ 2 = 12 ^ 2 + 9 ^ 2 = 144 + 81 = 225;

AB = √225 = 15 cm.

Answer: In this example, the conditions of the Pythagorean theorem are not met, so it can be argued that this triangle is not right-angled.