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.

3 + 4 + 5 = 12, so to work out the length of each side, we need to work out 72 divided by 12. 72/12 = 6. 6 x 3 = 18, 6 x 4 = 24, 6 x 5 = 30.This means that the sides have lengths 18 cm, 24 cm and 30 cm.The hypotenuse of a triangle is always the longest side. In this question, the side that is 30 cm must be the hypotenuse. Let us call the base A and the height B. Since this is a right-angled triangle, the base is equal to one side of the triangle and the height is equal to the adjacent side which is not the hypotenuse. To work out the area of a triangle, we use the formula Area = (A + B)/2.In this question, A and B are equal to 18 and 24. 18 + 24 = 42. 42/2 is 21, so the area of the triangle is 21 cm squared.