Q. 64.5( 15 Votes )

# 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.

Answer :

**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 = 10^{2} × 9 × 3 × √7 cm^{2}

Area = 2700√7 cm^{2}

**Hence, the area of the triangular field is 2700√7 cm ^{2}.**

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