A large panel needs to be moved through a corridor, the panel is tall as the corridor. The corridor is A feet wide before a right angle turn, after the turn, it is B feet wide. What is the maximum length of the panel that can pass through this corner.

Overhead view of the hallway:

+------------+---
|           /   |
|          /    |B ft
|         /     |
|        /+------
|       / |
|      /  |
|     /   |
|    /    |
|   /     |
|  /      |
| /       |
|/        |
+<-A ft-->|

as the board round the corridor it eventually becomes a 45-45-90 triangle with the corner and adjoining walls, two more 45-45-90 triangles are madee with sides A and sides B, so the length of the board equals the sum of the hypotenuses of the smaller triangles. the A side triangles hyp =A��2 and the B sides = B��2

SO we just have to add them together. A��2+B��2 is our board!
anyway, a board that tight of a fit is a pain in the ass to move around a hallway especially when human bodies are getting the way of moving it, so it works in theory but in practice a larger hallway, or smaller board should be used.