Tyler is tiling the floor of his 12 foot by 16 foot living room. He plans to place one-foot by one-foot square tiles to form a border along the edges of the room and to fill in the rest of the floor with two-foot by two-foot square tiles. How many tiles will he use?

Respuesta :

Answer:

It depends.

24 1x1 tiles, 8 2x2 tiles, and 32 total tiles.

Step-by-step explanation:

Tyler's living room is 12 feet by 16 feet.

That means that he can place 12 1x1 tiles along 2 sides, and 12 1x1 tiles along the other (since there are 4 tiles shared by 2 sides).

This would create an area of [tex]12 - 2[/tex] feet by [tex]16 - 2[/tex] feet, or [tex]10[/tex] feet by [tex]14[/tex] feet.

Since Tyler is using 2x2 tiles for the inner area, he would be able to place [tex]\frac{10}{2}=5[/tex] tiles on two sides and [tex]\frac{14}{2}-4=7-4=3[/tex] tiles along the other (since, once again, 4 tiles will be shared between 2 sides).

Adding them up, we get [tex]5+3=8[/tex] of the 2x2 tiles and [tex]12+12=24[/tex] of the 1x1 tiles.

If you're adding ALL of the tiles, then that would be a grand total of [tex]8+24=32[/tex] tiles.