## Question

### Solution

Correct option is

12 sq. units

The given inequality is equivalent to the following system of inequalities. (Fig)

2x + 3y ≤ 6, when x ≥ 0, y ≥ 0

2x – 3y ≤ 6, when x ≥ 0, y ≤ 0

–2x + 3y ≤ 6, when x ≤ 0, y ≥ 0

–2x – 3y ≤ 6, when x ≤ 0, y ≤ 0

Which represents a rhombus with sides

2x ± 3y = 6 and 2x ± 3y = –6

Length of the diagonals is 6 and 4 units along x-axis and y-axis.

∴         The required area = 1/2 × 6 × 4 = 12 sq. units. #### SIMILAR QUESTIONS

Q1

The diagonals of a parallelogram PQRS are long the lines

x + 3y = 4 and 6x – 2y = 7, then PQRS must be a

Q2

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Q3

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Q4

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Q5

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Q6

If abc are unequal and different from 1 such that the points are collinear, then

Q7

If two vertices of a triangle are (–2, 3) and (5, –1), orthocentre lies at the origin and centroid on the line x + y = 7, then the third vertex lies at

Q8

The line L has intercepts a and b on the coordinate axes. The coordinate axes are rotated through a fixed angle, keeping the origin fixed. If p andq are the intercepts of the line L on the new axes, then Q9

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Q10

Let O be the origin, A (1, 0) and B (0, 1) and P (xy) are points such thatxy > 0 and x + y < 1, then