Question

The perimeter of a right-angled triangle is 96 cm.

The lengths of its sides are in the ratio 6: 8:10
Work out the area of the triangle in cmp.

Answer 1

Perimeter = the sum of all the sides. In this case, we know the ratio but not what each would be multiplied by, hence the variable.

6x + 8x + 10x = 96

24x = 96

x = 4

6(4) = 24

8(4) = 32

10(4) = 40

Check:

24 + 32 + 40 = 96 cm

Area = (base * height) / 2

Base = 32

Height = 24

(The base and height are interchangeable here, as we just have to make sure we're multiplying the legs of the triangle together and avoiding the hypotenuse.)

(32 * 24) / 2

768 / 2

384

Area = 384 cm^2

Hope this helps!