## The perimeter of Triangle ABC is 20 cm. AB = 7 cm. BC = 4 cm. Determine whether triangle ABC is a right-angled triangle.

We know the perimeter of the triangle is 20cm, and we also know the lengths of two of the triangle's sides, AB = 7cm and BC = 4cm. By subtracting the known lengths from the perimeter, we can calculate the length of the third side (AC): 20 - 7 - 4 = 9 As a result, the length of AC is 9. If ABC were a right angle triangle, we could apply Pythagoras' Theorem to get the length of AC. Because it is the longest length, AC is the hypotenuse of the triangle. The Theorem of Pythagoras: a2 + b2 = c242 + 72 = 16 + 49 = 65 In the case where AC = c, c2 = 65 When c = 9, c2 = 81; nevertheless, when Pythagoras is used, c2 = 65. As a result, Pythagoras' Theorem is invalid, and the triangle ABC is not a right-angle triangle.