The space above the fireplace's mantel is 45 inches tall and 60 inches wide. You have the option of placing a 60", 68", 75" or 80" TV. Which is the largest TV that will fit? Show all your steps and reasoning for full credit.

To determine the largest TV that will fit above the fireplace's mantel, we need to consider both the height and width of the available space.

The height of the space is 45 inches. We need to find a TV that has a height equal to or smaller than this value.

Let's now consider each option:

1. 60" TV:
The height of the 60" TV will determine if it fits. Since the TV's height is not explicitly provided, we cannot determine if it is smaller than or equal to 45 inches.

2. 68" TV:
Again, we are not provided with the height of the 68" TV, so we cannot determine if it fits within the available 45-inch height.

3. 75" TV:
Similarly, without the height of the 75" TV, we cannot determine if it fits below the 45-inch height limitation.

4. 80" TV:
The height of the 80" TV will be the deciding factor. If this TV's height is 45 inches or smaller, it will fit above the mantel.

Unfortunately, we do not have information on the height of any of the TVs provided. Therefore, without this crucial information, we are unable to determine the largest TV that will fit above the fireplace's mantel.