Question

the perimeter of a triangular field is 420 metre and its sides are in ratio 6:7:8. find the area of the triangular field​

Answer 1

let the side be 6x,7x,8x

perimeter = 420m

sum of sides = 420m

6x+7x+8x = 420m

21x =420m

x= 20m

hence the sides are

6x= 6×20 = 120 m

7x = 7×20= 140m

8x = 8×20= 160m

here we dont know what is the base and height so,

by using heron formula

s = half of perimeter = 420/2= 210m

area =√(s(s-a)(s-b)(s-c))

= √(210(210-120)(210-140)(210-160))

= √(210×90×70×50)

= √(10000×7×3×3×3×7×5)

= 100×21√15

= 2100√15 m²