Answer & Solution
Answer: Option B
Solution:
$$\eqalign{
& 3x + 4y - 24 = 0 \cr
& \Rightarrow 3x + 4y = 24 \cr
& \Rightarrow \frac{{3x}}{{24}} + \frac{{4y}}{{24}} = 1 \cr
& \Rightarrow \frac{x}{8} + \frac{y}{6} = 1 \cr
& {\text{Area of }}\Delta OAB = \frac{1}{2} \times 6 \times 8 = 24{\text{ sq}}{\text{. units}} \cr
& {\text{And,}} \cr
& x + y + 4 = 0 \cr
& \Rightarrow x + y = - 4 \cr
& \Rightarrow \frac{x}{{\left( { - 4} \right)}} + \frac{y}{{\left( { - 4} \right)}} = 1 \cr} $$
$$\eqalign{ & {\text{Area of }}\Delta OCD = \frac{1}{2} \times 4 \times 4 = 8{\text{ sq}}{\text{. units}} \cr & \therefore {\text{Area of }}\Delta OCD = \frac{1}{3}{\text{Area of }}\Delta OAB \cr} $$
