Answer
The diagonal has a length of $ e\sqrt3$
Work Step by Step
We first find the diagonal of a the base of the cube. Since it is part of a 45-45-90 triangle containing a side, its length is: $e\sqrt{2}$. We call d the diagonal. Thus:
$ d^2 = e^2 + (e\sqrt{2})^2 \\ d^2 = 3e^2 \\ d = e\sqrt3$
