# 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

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Determining a determinant63 mins
Determinants of Matrices of different order59 mins
Types of Matrices & Properties51 mins
Interactive Quiz on Matrices and Determinants41 mins
Interactive Quiz on Properties of Determinants43 mins
Lecture on Product of Determinants58 mins
Triangular Matrices & operations on matrices58 mins