Compare the area of the room and of the tiles. Be careful with the units.
Number of Tiles: 1440 Explanation: See solution.
Practice makes perfect
Note that the dimensions of the room and the tiles are given in different units. To compare the areas, we first must convert the measurements of the room to inches. Recall that there are 12 inches in a foot.
Side
Measurement
In feet
In inches
Length
20
20* 12=240
Width
12.5
12.5* 12=150
Calculating the area of the room.
To find the area of the room, we can use the formula for the area of a rectangle in terms of its length l and width w.
A=l wWe calculate the area in square inches.
The floor area of the room is 36000 square inches.
Calculating the area of a tile.
Let's see now how much we can cover with a single 5-inch square tile. The find the area of a tile, we can use the formula for the area of a square in terms of its side length, s.
A=s^2
We calculate the area in square inches.
Since one tile covers 25 square inches and we need to cover 36000 square inches, we need at least 36000/25=1440 tiles. You can see these 1440 tiles covering the floor on the figure below.
Alternative Solution
Alternative way of thinking
Instead of investigating areas, we can try to cover the room with the tiles starting from the sides. Let's think of how many 5-inch square tiles we need in a line to fill the length of the sides.
Side
Measurement in inches
Tiles needed
Length
240
240/5=48
Width
150
150/5=30
This means that in a rectangular pattern we need 30 rows of tiles with 48 tiles in each row to cover the floor of the room. Thus, we need 30* 48=1440 tiles.
