The perimeter of a triangular field is 420 m and its sides are in the ratio 6:7:8. Find the area of the triangular field.
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