Tetrahedra Tester

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
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Problem

An irregular tetrahedron is composed of four different triangles.

Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

How many different tetrahedra can be constructed?

Explain how you know you have found all the possible tetrahedra.