The sides of a triangle are in the ratio 4 : 3 : 2.  The perimeter of the triangle is 36 cm.  The area (in cm²) of the triangle is?

12\(\sqrt {15}\)

Ratio of sides:

A  :  B  :  C  ⇒  Perimeter

4  :  3  :  2  ⇒       9

Here, 9x = 36

⇒ x = 4

Sides are ⇒ 16, 12, 8

Semi perimeter (s) = \(\frac{36}{2}\) = 18

Now,

Area of triangle   = \(\sqrt {s(s - a) (s - b) (s - c)}\)

                           = \(\sqrt {18(18 - 16) (18 - 12) (18 - 8)}\)

                           =  \(\sqrt {18 × 2 × 6 × 10}\)

                           =  \(\sqrt {9 × (2 × 2) × 5 × 3 × (2 × 2)}\)

                           = 12\(\sqrt {15}\)