Triangle ABC has perimeter 20 cm. AB = 7 cm. BC = 4 cm. By calculation, deduce whether triangle ABC is a right-angled triangle. 4 marks.

We know that the perimeter of the triangle is 20cm and we also know the value of two of the sides of the triangle, AB=7cm and BC=4cm. We can work out the length of the third side (AC) by subtracting the known lengths from the perimeter:20 - 7 - 4 = 9 Therefore, the length AC is 9.If ABC were a right angle triangle, we'd be able to use Pythagoras's Theorem to work out the length AC. AC is the hypotenuse of the triangle because it is the longest length.Pythagoras's Theorem: a² + b² = c²4² + 7² = 16 + 49 = 65Where AC = c, c² = 65 If c = 9, then c² = 81, however when using Pythagoras, c² = 65.Therefore, Pythagoras's Theorem cannot be use and the triangle ABC is not a right-angle triangle.