question_answer

The area of the triangle formed by the two lines and the x-axis is:

A) 4 sq. units

B) 6 sq. units

C) 8 sq. units

D) 12 sq. units

Correct Answer: D

Solution :

Let us plot the graph of the lines given by the equations

\[4x-3y=-4\] and \[4x+3y=20.\].

For equation \[4x-3y=-4\]

x \[-1\] 2 5 y 0 4 8

For equation \[4x+3y=20\]

x \[-1\] 2 5 y 8 4 0

Plotting these points on the same graph paper, we get the following graph:

The vertices of the triangle formed by the two lines and the x-axis are \[(-1,0),\,\,(2,4)\] and \[(5,0)\].

Area of triangle formed by the two lines and the X-axis is shaded and given by

\[\frac{1}{2}\times AQ\times h=\frac{1}{2}\times 6\times 4=12\,sq.\,units\]

So option [d] is correct.