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 which TV will fit above the fireplace's mantel, we need to consider both the height and width of the space above.

The height of the space is 45 inches, and we need to ensure that the TV's height does not exceed this limit.

- The 60" TV has a height of 60 inches, which exceeds the 45-inch height limit.
- The 68" TV has a height of 68 inches, which also exceeds the 45-inch height limit.
- The 75" TV has a height of 75 inches, exceeding the height limit as well.
- The 80" TV has a height of 80 inches, which is greater than the 45-inch height limit.

Therefore, the largest TV that will fit and not exceed the height limit is the 75" TV.