Final answer:
The dimensions of the new rug for the hotel's dining room, which is 45 feet by 37 feet, would be 39 feet by 31 feet after allowing for a 3-foot wood-floor border.
Step-by-step explanation:
The dining room in the hotel is a rectangle measuring approximately 45 feet by 37 feet. If we need to have a 3 feet wide strip of wood floor visible around the outside of the rug, we must subtract 6 feet from both the length and the width of the room to calculate the dimensions of the new rug (3 feet on each side).
Therefore, the length of the new rug will be 45 feet - 6 feet = 39 feet, and the width will be 37 feet - 6 feet = 31 feet.
The dimensions of the new rug for the dining room would be 39 feet by 31 feet to maintain the 3 feet of wood floor visible around the perimeter of the rug.