Question

The Yoshidas are planning to install ceramic floor is a small hallway. The hallway measures 4 feet by 12 feet. Tiles are squares measuring 3,6,9, or 12 inches on each side. Which tile can the Yoshidas use without having to cut any of them to fit?

Answer 1

4 ft = 48 inches

48/3 = 16
48/6 = 8
48/9 = 5+something
48/12 = 4

We have ruled out 9" tiles

See if the remaining three sizes will fit on the 12-foot side.

Answer 2

it looks like they can use any tiles except the nine inch ones. likely the best option is the 12 inch ones. every 12 inch tile is a perfect square, and its one foot on each side. Since both dimensions (length and width) are divisble into 1 foot sections, 12 inch tiles can be used. Similar reasoning can be used to prove that the 3 and 6 inch tiles work. every 4 six-inch tiles makes a 12 inch tile, and every 16 three-inch tiles make a 12 inch tile. just remember youre working with areas and squares

Answer 3

Well, maybe. You can make cooler patterns with the smaller tiles.