Pythagorus’ theorem

Question

Triangle ABC has perimeter 18cm

AB= 7cm

BC= 3cm

By calculation, deduce whether triangle ABC is a right-angled triangle.

Answer 1

To start, we know that the 3 sides add up to the perimeter of 18cm. We can use this to find the length of the 3rd side, CA.

AB + BC + CA = 18

7 + 3 + CA = 18

10 + CA = 18

CA = 8

The pythagorean theorem states that in a right triangle a² + b² = c², where c is the length of the hypotenuse (the longest side opposite to the right angle) and a and b are the lengths of the other two sides.

In this problem we can replace a with 7, the length of AB, b with 3, the length of BC, and c with 8, the length of CA.

a² + b² = c²

7² + 3² = 8²

49 + 9 = 64

58 = 64

Since the equation is not true, we can deduce that ABC is NOT a right triangle.