The perimeter of a triangular field is 420 m and its sides are in the

1.	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.
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

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.

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