In a convex quadrilateral $ABCD$, it is given that $E$ is the intersection of the diagonals, triangles $ADE, BCE, CDE$ have areas of $12 \, \text{cm}^2, 45 \, \text{cm}^2, 18 \, \text{cm}^2$ respectively, and the length of side $AB$ is $7 \, \text{cm}$.

Determine the distance from point $D$ to the line $AB$.

(M. Petrová)