Consider a box l x b x h

let x = width of one corridor.

let y = width of the perpendicular corridor.

We will disregard the height of the box here since I assume that you can find out the correct way to orient the box.

The box will fit throught the hallway if:

(sqrt(x^2+y^2) - l/2) >= b

I will post the reasoning after I get out of my office.

BTW, thanks for posting this intersting problem.