Question 7
$H$ is a point on the side $BC$ of a square $ABCD$. $F$ is a point outside $ABCD$ such that the side $AB$ intersects $FD$ at $E$ and $FH$ at $G$, where $DE:EF=5:3$ and $GH:FG=5:4$. If the areas of triangles $ADE$, $EFG$ and $BGH$ are the same, find the ratio of the area of $DEGH$ to the area of $CDH$.
