You have the correct steps and final answer. The area of the room is 196 square feet, so each side is sqrt(196) = 14. The perimeter is 14*4 = 56 feet. You'll need 6 boards (each 10 ft long) to get 60 ft total. You'll have 60-56 = 4 ft of board left over. This is assuming that there isn't any other type of waste or mistakes made in cutting.
Nice work on getting the correct steps and final answer.