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?
1 foot
2 feet
4 feet
8 feet
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?
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To find the largest square tile that can cover the floor without overlap or cutting, you need to determine the greatest common divisor (GCD) of the room’s dimensions, which are 12 feet and 8 feet.
1. The factors of 12 are: 1, 2, 3, 4, 6, 12
2. The factors of 8 are: 1, 2, 4, 8
The common factors of 12 and 8 are 1, 2, and 4. The largest of these common factors is 4.
Therefore, the side measure of the largest square tile that you can use is 4 feet.
This means you can lay tiles that are 4 feet by 4 feet in size, covering the entire area of the room (which is 96 square feet). Great job! If you have more questions, feel free to ask!