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Question

Draw the graph of the equations x = 3 , x = 5 and 2x − y − 4 = 0 . Also, find the area of the quadrilateral formed by the lines and the x-axis.

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Solution

The given equations are
x = 3 .....(i)
x = 5 .....(ii)
2x − y − 4 = 0 .....(iii)
For (iii), we have
x 0 2
y −4 0

We plot the lines on the graph as follows:

The vertices of the quadrilateral thus formed are A(5, 0), B(5, 6), C(3, 2) and D(3, 0).
∴ Area of the quadrilateral DABC
= Area of a trapezium
= 12ha+b
=12×2×2+6=8 square units
Thus, the area of the quadrilateral formed by the given lines and the x-axis is 8 square units.

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