The perimeter of a triangular field is 540 m and its sides are in the ratio
Question:

The perimeter of a triangular field is 540 m and its sides are in the ratio 25: 17: 12. Find the area of triangle.

Solution:

Let the sides of the given triangle be a = 25x, b = 17x, c = 12x respectively,

So,

a = 25x cm

b = 17x cm

c = 12x cm

Given Perimeter = 540 cm

2s = a + b + c

a + b + c = 540 cm

25x + 17x + 12x = 540 cm

54x = 540 cm

x = 10 cm

Therefore, the sides of a triangle are

a = 250 cm

b = 170 cm

c = 120 cm

Now, Semi perimeter s = (a + b + c)/2

= 540/2

= 270 cm

By using Heron’s Formula

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

$=\sqrt{270 \times(270-250) \times(270-170) \times(270-120)}$

$=9000 \mathrm{~cm}^{2}$

Therefore, the area of the triangle is $9000 \mathrm{~cm}^{2}$