Given a pyramid with square base ABCD and a vertex V.
Suppose VA = a, VB = b, VC = c and VD = d.
Determine AB in terms of a, b, c and d.

First Question:
Is the problem well-defined?

Answer:
The answer is negative.
Consider the case where a = b = c = d.
The size of the base can vary feely.
It seems that the height of the pyramid should also be given in order to restrict the size of the square base.

What is next?
Suppose a, b, c and d are given, together with the volume of the pyramid.
Then the problem is meaningful because there is a formula which determines the volume and a tetrahedron once the length of the 6 sides are known.
This problem can be easily solved by cutting the pyramid into two tetrahedra.