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.