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 = 102 × 9 × 3 × √7 cm2


Area = 2700√7 cm2


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


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