Question

The perimeter of a triangular field is 420m and it's sides are in the ratio 6:7:8 .Find the area of triangular field . Without using the herons formula .​

Answer 1

(Sum of all sides)/2 = Perimeter of ∆

let each part of side be y

so,

(6x+7x+8x)/2 = 420

6x + 7x + 8x = 420 * 2 = 840

21x = 840

x = 40 cm

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so , Sides are :

6x = 6(40) = 240 cm (Base or, Height)

7x = 7(40) = 280 cm (Base or, Height)

8x = 8(40) = 320 cm (Hypotenuse)

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so ,

Area of ∆ = (½) bh

so ,

Area = (½) (240)(280) = 120(280)

Area of ∆ = 33,600 cm² .

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