In the given figure, if AD = 3, DE = 4, AB = 12, BF = 2, FG = 6, BC = 10, then the value of M N is: (Assume: M is the area of the quadrilateral FGDE and N is the area of the triangle ABC.)

In the given figure, if AD = 3, DE = 4, AB = 12, BF = 2, FG = 6, BC = 10, then the value of $$\frac{\text{M}}{\text{N}}$$ is: (Assume: M is the area of the quadrilateral FGDE and N is the area of the triangle ABC.)

Answer: Option A

Solution

Answer: Option A

Solution:

$$\begin{array}{rl}& \text{Area of }\Delta ABC=\frac{1}{2}\sin \theta \times 12\times 10\\ & \text{Let }\frac{1}{2}\sin \theta =x\\ & \text{Area of }\Delta ABC=120x\\ & \text{Same as,}\\ & \text{Area of }\Delta BEF=10x\\ & \text{Area of }\Delta BDG=9\times 8x=72x\\ & M=72x-10x=62x\\ & N=120x\\ & \frac{M}{N}=\frac{62x}{120x}=\frac{31}{60}\end{array}$$