The area of the square is given as 63504 m², and we need to determine how much time a man will take to complete one round along the boundary if he cycles at a constant speed of 26.88 km/h.

To solve this problem, we can follow the steps below:

Step 1: Calculate the side length of the square
The area of a square is given by the formula: Area = side length * side length.
Therefore, we can find the side length of the square by taking the square root of the given area.
Side length = sqrt(63504) = 252 meters.

Step 2: Calculate the perimeter of the square
The perimeter of a square is given by the formula: Perimeter = 4 * side length.
Therefore, the perimeter of this square is: Perimeter = 4 * 252 = 1008 meters.

Step 3: Convert the speed from km/h to m/s
To calculate the time taken, we need to have the speed in meters per second (m/s).
We know that 1 km = 1000 m and 1 hour = 3600 seconds.
Therefore, the speed in m/s is: 26.88 km/h * (1000 m/km) / (3600 s/h) = 7.4667 m/s (approximately).

Step 4: Calculate the time taken to complete one round
The time taken to complete one round along the boundary of the square can be calculated using the formula: Time = Distance / Speed.
In this case, the distance is equal to the perimeter of the square, which is 1008 meters, and the speed is 7.4667 m/s.
Therefore, the time taken to complete one round is: Time = 1008 m / 7.4667 m/s ≈ 135.08 seconds.

Answer:
The man will take approximately 135.08 seconds (or 2 minutes and 15.08 seconds) to complete one round along the boundary of the square.