You want to lay tile in a room of your house. the room is 12 feet by 8 feet. what is the side measure of the largest square tile that you can use to cover the whole floor so there is no overlap or cutting?

4 feet
Tiles 4 feet by 4 feet will fill up the entire 96 sq ft area in just six tiles; three rows and two columns of them. A tile with the dimensions of 4 x 4 has an area of 16 sq ft, which divides evenly in 96 (96/16=4). 16 is the largest square that divides into 96, making it the largest square tile that can be used to cover the entire floor smoothly without cutting. The side length is 4, so the answer is 4 feet.