First slide

Equation of line in Straight lines

Question

The area of the region enclosed by 4 |x| + 5 |y| ≤ 20 is

Moderate

A

10
B

20
C

40
D

none of these

Solution

The four lines enclosing the given region are 4x + 5y = 20, 4x – 5y = 20, – 4x + 5y = 20 and – 4x – 5y = 20. Clearly, the four lines form a rhombus having diagonals of length 10 and 8.
$∴$ Required area $= \frac{1}{2} \times 10 \times 8 = 40$

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