The perimeter of a right-angled triangle is 72 cm. The lengths of its sides are in the ratio 3 : 4 : 5. Work out the area of the triangle.

As we know the ratio of the sides is 3:4:5, label the sides x,y and z respectively. Side x is of length (3/12)*72, side y is of length (4/12)*72 and side z is of length (5/12)72. Giving, x = 18cm, y = 24cm, z = 30cm. Observe x is the base and z is the hypotenuse. Area of a triangle is (base x height)/2. Area = (1824)/2 = 216cm^2