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.

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