Box in box

There are two rectangular boxes, A and B. Box A fits completely inside box B. Show that the sum of the three side lengths of A is less than or equal to the sum of the three side lengths of B.

Comment

When I was a PhD student, I worked as a teaching assistant for Prof. Yusuke Nakamura class. This problem appeared in an undergraduate exercise. I could not solve it at all, but I think some students were able to solve it.

A great explanation can also be found in this Ebima Lab’ YouTube video (in Japanese but English subtitles are available).