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.

The equation for the area of a triangle is 1/2 x base x height
So, first we need to know the length of the base and the height of the triangle.
We know that the perimeter of the triangle is 72cm, and the ratio of the sides is 3 : 4 : 5. To work out the length of the three sides, we add up each part of the ratio (3 + 4 + 5 = 12), and divide the perimeter by it (72 / 12 = 6).
Then we multiply each part of the ratio by 6, so we have the sides being 18 : 24 : 30. We can check that these total 72.
Now, the hypotenuse of the triangle is always the longest side; and since it is a right angled triangle we know that one of the sides will be the base and one will be the height. Note that because the original equation has us multiplying the two values, it does not matter which is which. So base = 3 x 6 = 18 and height = 4 x 6 = 24, or vice versa.
Putting these back into the equation, we have area = 1/2 x 18 x 24 = 216cm²