Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540cm. Find its area.

We know that, 

The Heron's formula for calculating the area of the triangle,

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

where, s is the semi-perimeter = half of the perimeter = 540/2 = 270

and  a, b and c are the sides of the triangle 

Triangular sides are, a = 12x, b = 17x, c = 25x

Thus, Semi-perimeter 

s = (a $+$ b $+$ c)/2

270 = (12x $+$ 17x $+$ 25x)/2

270 = 54x/2

540 = 54x

x = 10cm

Triangular sides are, a = 12x = 120

 b = 17x = 170

c = 25x = 250

Area of a triangle  =  $\sqrt{270(270 - 120)(270 - 170)(270 - 250}$)

= $\sqrt{270 \times 150 \times 100 \times 20}$

= $\sqrt{81000000}$

= 9000 cm²

Hence, Area of the triangle = 9000 cm²