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.

Consider a right angled triangle, it has perimeter of 72cm. Let's label the three sides a, b and c.Therefore, a + b + c = 72cm.Also, we know that a:b:c = 3:4:5Therefore we can say that a = 3x, b = 4x, c = 5x.Substituting this into the original equation we get:3x + 4x + 5x = 7212x = 72, therefore x = 6.So the sides a, b and c have length 18cm, 24cm and 30cm respectively.Now we can find the area A, which is A = 0.5a*b for a right angled triangle.This gives A = 0.5 * 18 * 24 = 216cm²