Question 15
In the following diagram, $ABC$ is a triangle and $D$ lies on $AB$ such that the ratio $|AD|:|DB|=3:4$. Points $E$ and $G$ lie on $AC$ and $BC$ respectively such that $DBGE$ is a parallelogram and $F$ is the intersection of $DC$ and $GE$. If the ratio of the area of $\triangle EDF$ to the area of $\triangle ABC$ is $m:n$, where the highest common factor of $m$ and $n$ is $1$, what is the value of $m+n$?
