Find the value of x if the area of a triangle is 35 square cms with vertices (x, 4), (2, – 6) and (5, 4).
Given: – Vertices of triangle are (x, 4), (2, – 6) and (5, 4) and area of triangle is 35 sq.cms
Tip: – If vertices of a triangle are (x1,y1), (x2,y2) and (x3,y3), then the area of the triangle is given by:
Now,
Substituting given value in above formula
⇒ 
Removing modulus
⇒ 
Expanding along R1
⇒ 
⇒ [x(– 10) – 4(– 3) + 1(8 – 30)] = ± 70
⇒ [ – 10x + 12 + 38] = ± 70
⇒ ±70 = – 10x + 50
Taking + ve sign, we get
⇒ + 70 = – 10x + 50
⇒ 10x = – 20
⇒ x = – 2
Taking – ve sign, we get
⇒ – 70 = – 10x + 50
⇒ 10x = 120
⇒ x = 12
Thus x = – 2, 12
6