A fly is in a cubical room of side 2m. It starts from one corner of the floor and goes to the centre of the ceiling. Unfortunately, the fly cannot fly. So it has to crawl along the floor, walls or ceiling to reach there. What is the length of the shortest path for the fly to reach there?

Answer : 

We have a cubical room of sides 2 m . 

Let fly start from corner ' A ' . 
And
C is the centre of the ceiling 

So the shortest path fly could take is A to B and B to C  . 

We know diagonals of square are same in length and they bisect each other .  So BC  =  $\frac{1}{2}$of the diagonal of square formed by Top of that cubical room . 

So ,

AB  =  2  m 

We know diagonal  of square  = $\sqrt{2}$ ( Side length ) 
So here length of diagonal BD  = 2$\sqrt{2}$ 
So,
BC  =  $\frac{1}{2}$ BD   =  $\frac{1}{2}$ ( 2$\sqrt{2}$  )  =  $\sqrt{2}$  m 
SO,
Length of shortest path for the fly to reach the centre of ceiling  =  AB  +  BC  =  ( 2  + ​ $\sqrt{2}$ ) m                   ( Ans )