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.

We know the perimiter is split into the proportions 3:4:5 therefore by adding 3+4+5 we can work out what fraction of 72cm each side is.Thus 3/(3+4+5) = 3/12 = 1/4 is the fraction of 72 that belongs to the shortest side. This means the shorest side has lenght of 1/4 * 72 = 18cm.We can repeat this to work out the lenght of the other two sides giving the middle sized side to have lenght 4/12 * 72 = 1/3 * 72 = 24cm.And the longest side lenght 5/12 * 72 = 30cm.
We can now draw and label a sketch of the triangle.As it is a right anlged triangle we can use the formular Area = 1/2 * Base * Height. Which gives 24 * 18 * 1/2 = 12 * 18 = 10 * 18 + 2 * 18 = 216cm²