Answer :

Given that the sides are in ratio of 6:7:8

Let the sides of the triangle be 6x, 7x and 8x.


Perimeter(Δ) = 420


6x + 7x + 8x = 420


21x = 420


x = 20


Therefore the sides are 120m, 140m and 160m.


a = 120, b = 140, c = 160


s = (a + b + c)/2


s = (120 + 140 + 160)/2 = 420/2 = 210.


Area(Δ) = √s(s-a)(s-b)(s-c)


Area(Δ) = √210(210-120)(210-140)(210-160)


Area(Δ) = √210×90×70×50


Area(Δ) = 2100√15 m2


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