So I'm using the REA Problem Solvers Physics book as an extra problems type book. I'm currently on Problem 12. I'll type out the whole problem just for clarity but I only need some direction on the last step, because they state an answer without any derivation.

== The crew of a spacecraft, which is out in space with the rocket motors switched off, experience no weight and can therefore glide through the air inside the craft.

The cabin of such a spaceship is a cube of side 15 ft. An astronaut working in one corner requires a tool which is in a cupboard in the diamaetrically opposite corner of the cabin. What is the minimum distance which she has to glide and at what angle to the floor must she launch herself?

If she decided instead to put on boots with magnetic soles which allow her to remain fixed to the metal of the cabin, and thus enable her to walk along the floor and, in the absence of gravitational effects, up that walls and across the ceiling, what is the minimum distance she needs to get to the cupboard? == As I stated before. I have no problem getting the required answers. So dont think I'm trying to get a easy out answer. At the end of the problem, they offer the following with no explanation to back it up.

There turns out to be three routes that one can take to the cupboard. I get that much, here is where I go astray... == In the first route, the astronaut crosses the floor and climbs, a "breadth" wall; in the second, he crosses the floor and climbs a "length" wall; and in the third he crosses neither floor nor ceiling, but climbs two different walls. In this particular problem, since the cabin is cubical, all these routes are of the same length. In a problem in which the length,l, breadth, b, and height, h, are all different, the three routes correspond to vectors having components (l ; b+h) , (b ; l+h) , and (h ; l+b). The shortest of these will be the one in which the x-component is the longest dimension and the y-component the sum of the other two. ==

The part where it is stated the components of these route vectors is where I dont understand how they come up with this. If anyone can give me a little shove in the right direction I would be most grateful.