Given are $5$ edge lengths $a,a,a,b,c$ of a tetrahedron. The three equal edges of length $a$ and the other edges $b,c,d$ are distributed as shown in the sketch. It is also given that $a\le b, a\le c, a\le d$. What is the length of the sixth edge $d$?
Edit: In a previous version the wrong sketch was shown. Now the right figure is shown.
Note:
It is simple if the figure would be planar, but it is a three-dimensional shape. Also the edges must be labelled as in the sketch else we would get a different tetrahedron.