x + 8y - 22 = 0, 5x + 2y - 34 = 0, 2x - 3y + 13 = 0 are the three sides of a triangle. The area of the triangle is

Question

x + 8y - 22 = 0, 5x + 2y - 34 = 0, 2x - 3y + 13 = 0 are the three sides of a triangle. The area of the triangle is (A) 36 square unit (B) 19 square unit (C) 42 square unit (D) 72 square unit

Tardigrade Admin · Accepted Answer

If AB denotes: x +8y -22 = 0 arrow (1) BC denotes: 5x +2y-34 = 0 arrow (2) and CA denotes: 2x +3y-13 = 0 arrow (3) Then solving equations (1), (2) and (3), we get A≡(-2, 3), B≡(6, 2) and C≡(4, 7). Hence, area of Δ ABc is 19 square units

Q. $x + 8 y - 22 = 0, 5 x + 2 y - 34 = 0, 2 x - 3 y + 13 = 0$ are the three sides of a triangle. The area of the triangle is

36 square unit

19 square unit

42 square unit

72 square unit

If AB denotes : $x + 8 y - 22 = 0 \to (1)$
BC denotes : $5 x + 2 y - 34 = 0 \to (2)$
and CA denotes : $2 x + 3 y - 13 = 0 \to (3)$
Then solving equations (1), (2) and (3), we get
$A \equiv (- 2, 3), B \equiv (6, 2)$ and $C \equiv (4, 7) .$
Hence, area of $Δ A B c$ is 19 square units

Q. x+8y−22=0,5x+2y−34=0,2x−3y+13=0 are the three sides of a triangle. The area of the triangle is