## Book: RD Sharma - Mathematics (Volume 2)

### Chapter: 21. Areas of Bounded Regions

#### Subject: Maths - Class 12th

##### Q. No. 30 of Exercise 21.3

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30
##### Using the method of integration, find the area of the region bounded by the following line 3x – y – 3 = 0, 2x + y – 12 = 0, x – 2y – 1 = 0.

To find region enclosed by

3x – y – 3 = 0 ...(i)

2x + y – 12 = 0 ...(ii)

x – 2y – 1 = 0 ...(iii)

Solving (i) and (ii), we get,

5x – 15 = 0

Or x = 3

y = 6

The points of intersection of (i) and (ii) is B (3,6)

Solving (i) and (iii), we get,

5x = 5

Or x = 1

y = 0

The points of intersection of (i) and (iii) is A (1,0)

Solving (ii) and (iii), we get,

5x = 25

Or x = 5

y = 2

The points of intersection of (ii) and (iii) is C (5,2) .

These are shown in the graph below: -

Area of the bounded region

=

= 11 sq. units

The area of the region bounded by the following line 3x – y 3 = 0, 2x + y – 12 = 0, x – 2y – 1 = 0 is

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