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.

Let x be a number so that the sides of the triangle are 3x, 4x and 5x, because the ratio is 3 : 4 : 5. The perimeter is 3x+4x+5x=12x=72, meaning that x = 72/12 = 6. The sides of the triangle are 36=18, 46=24 and 56=30. As the hypotenuse is the longest side, that is 30, and 18 and 24 are the lengths of the legs. As the area of a right triangle is the product of the legs divided by 2, that is 1824/2=216