The ratio of the sides of the triangle are given as 12 : 17 : 25

Now, let the common ratio between the sides of the triangle be “x”

∴ The sides are 12x, 17x and 25x

It is also given that the perimeter of the triangle = 540 cm

12x + 17x + 25x = 540 cm

54x = 540cm

x = 10

Now, the sides of triangle are 120 cm, 170 cm, 250 cm.

So, the semi perimeter of the triangle (s) = 540/2 = 270 cm

Using Heron’s formula,

Area of the triangle

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

= \(\sqrt{270(270 - 120)(270 - 170)(270 - 250)}cm^2\)

= \(\sqrt{270 \times 150 \times 100 \times 20}cm^2\)

= 9000\(cm^2\)