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

Perimeter= 72Ratios are 3:4:5In total, you can think of there being 3+4+5=12 "portions".This means that in the perimeter includes 12 portions. 72/12=6 so each portion is worth 6cm.
Now we can work out the length of each side.3:4:5 scaled up by 6 (recall that each portion is worth 6cm) yields sides of lengths 18cm, 24cm and 30 cm.
Note that the question says that it is a right angled triangle, therefore, we can use the formula for the area of a right angled triangle (1/2 x a x b).
Does it matter what you set a and b as? Yes, because neither a nor b are the hypotenuse. In our triangle, the hypotenuse will be 30cm (the longest length) so our a and b must be 18 and 24.
1/2 x 18 x 24 = 216cm^2