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.

So, working out the different side lengths of the triangle is going to help find the area at the end. We split the ratio up into 3s and show them as a proportion of the whole perimeter. For example, one side length is 3/12 of 72, the second is 4/12 of 72 ans the third is 5/12 of 72, meaning the lengths of the sides are 18cm, 24cm and 30cm. Now, to find the area, we can construct this triangle since we are told it is a right angles triangle with the 30cm line being the hypoteneuse (the diagonal), and the 18cm and 24cm lines the base and height of the triangle. So using the formula, Area = (base x height)/2, the area is 216cm^2