The perimeter of a triangular field is 420 cm, and its sides are in the ratio 2:2:3. Find the area of the triangular field.

Given: Perimeter of triangular field = 420 cm

Sides are in ratio 2:2:3

To Find: Area of the triangular field

Concept Used:

If sides of a triangle are a, b, and c, then area of a triangle is given by:

Where s = semiperimeter of the triangle

The perimeter of triangle = Sum of sides of the triangle

Assumption: Let the sides of triangle be

a = 2x

b = 2x

c = 3x

Explanation:

Perimeter = 2x + 2x + 3x = 7x

Perimeter = 420 cm

7x = 420

x = 60 cm

Hence, the sides of the triangle are:

a = 2 × 60 cm = 120 cm

b = 2 × 60 cm = 120 cm

c = 3 × 60 cm = 180 cm

s = 210 cm

Area = 10² × 9 × 3 × √7 cm²

Area = 2700√7 cm²

Hence, the area of the triangular field is 2700√7 cm².