Geo Meteor!

In a triangle $ABC$ , it is given that $BC= 12 \text{ cm}$ , $AC =13 \text{ cm}$ and $(AB)^2=31 \text{ cm}^2$ . If $AE$ is the altitude and $AD$ the median from $A$ , find $ED$ .

If $x$ is the solution, submit $12x$ as your answer.