# Rectangular prisms!

Algebra Level 4

Given a rectangular prism (as shown below) whose edge lengths have a sum of 36, what is the minimum value for the length of the line connecting two vertices which do not share a face?

If the minimum value can be expressed as $$a\sqrt{b}$$, where $$a$$ and $$b$$ are integers with $$b$$ square-free, submit your answer as $$a+b$$.

×