Spot, the Marching Soldiers Dog

From rec.puzzles

A body of soldiers form a 50m-by-50m square ABCD on the parade ground. In a unit of time, they march forward 50m in formation to take up the position DCEF. The army's mascot, a small dog [named “Spot”], is standing next to its handler at location A.

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Fig 1: The body of soldiers

When the soldiers start marching, the dog begins to run around the moving body in a clockwise direction, keeping as close to it as possible. When one unit of time has elapsed, the dog has made one complete circuit and has got back to its handler, who is now at location D. (We can assume the dog runs at a constant speed and does not delay when turning the corners.)

How far does the dog travel?