Question

The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is ______.

पर्याय

• (a + b + c)²

• 0

• a + b + c

• abc

Answer 1

The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is 0.

Explanation:

Let the vertices of a triangle are, A ≡ (x₁, y₁) ≡ (a, b + c)

B ≡ (x₂, y₂) ≡ (b, c + a) and C = (x₃, y₃) ≡ (c, a + b)

∵ Area of ΔABC = Δ = `1/2[x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)]`

∴ Δ = `1/2[a(c + a - a - b) + b(a + b - b - c) + c(b + c - c - a)]`

= `1/2[a(c - b) + b(a - c) + c(b - a)]`

= `1/2(ac - ab + ab - bc + bc - ac)`

= `1/2(0)`

= 0

Hence, the required area of triangle is 0.