Find the length of the longest pole that can be put in a room of dimensions 10m * 10m * 5m.
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The longest pole that can be put in a room will be at the diagonal of this room (cuboid).

And the diagonal of cuboid is given by, D = (l² + b² + h²)^1/2    (i.e. square root of the sum of the squares of the l,b,h)

Hence D = (10² + 10² + 5²)^1/2  
               = (100 + 100 + 25)^1/2
               = (225)^1/2 
               = 15

Hence 15 m will be the longest pole that can be placed in the room of the given dimensions.