Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

As $\frac{1}{x} = 3.5 = \frac{7}{2}$, so $x = \frac{2}{7}$.
Then $x+2 = \frac{16}{7}$.
Hence $\frac{1}{x+2} = \frac{7}{16}$.