﻿ The area enclosed by 2|x| + 3|y| ≤ 6 is : Kaysons Education

# The Area Enclosed By 2|x| + 3|y| ≤ 6 Is

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## 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.

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