Question 1049223: Ms. Rivera wishes to tile her classroom floor with square tiles. She wants to be able to use whole tiles, without cutting any pieces. The rectangular floor has dimensions 8.4 meters by 7.2 meters. What is the minimum number of whole identical square tiles required and what are the dimensions of each tile?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! A whole number of tiles will need be lined up along one of the 7.2-meter sides of the room.
Squaring that number, you would have enough tiles to cover a 7.2 m by 7.2 m square portion of the room. Since 8.4 m - 7.2 m = 1.2 m, a rectangle,
measuring 7.2 m by 1.2 m would remain to be covered.
Since 7.2 m ÷ 1.2 m = 6 , that space can be covered with 6 tiles measuring 1.2 m by 1.2 m. Those 6 tiles would be lined up against one 7.2-meter long side of the room, so another 6 tiles would fill the other 7.2-m length, and  tiles would cover the 7.2 by 7.2 m square part. That is
 tiles, each measuring  .
ANOTHER WAY:
Measured in decimeters, the room measures 72 by 84.
Maximum common divisor of 72 and 84 is 12.
84 = 12 × 7 and 72 = 12 × 6.
Using tiles measuring 12 decimeters = ,
 tiles could be lined up along the shorter side of the room,
and  tiles could be lined along the longer side of the room,
Leaving no gaps.
That means that the whole room would be covered by rows of tiles.
That is  tiles.
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