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Problem 2
Tiles. A restaurant owner is replacing the restaurant's bathroom floor with square tiles. The tiles will be laid side-by-side to cover the entire bathroom with no gaps, and none of the tiles can be cut. The floor is a rectangle that measures 24 feet by 18 feet.
a. What is the largest possible tile size she could use? Write the side length in feet. Explain how you know it's the largest possible tile.
b. How many of these largest size tiles are needed?
c. Name more tile sizes that are whole number of feet that she could use to cover the bathroom floor. Write the side lengths (in feet) of the square tiles.

Problem $2$ $\newline$ Tiles. A restaurant owner is replacing the restaurant's bathroom floor with square tiles. The tiles will be laid side-by-side to cover the entire bathroom with no gaps, and none of the tiles can be cut. The floor is a rectangle that measures $24$ feet by $18$ feet. $\newline$ a. What is the largest possible tile size she could use? Write the side length in feet. Explain how you know it's the largest possible tile. $\newline$ b. How many of these largest size tiles are needed? $\newline$ c. Name more tile sizes that are whole number of feet that she could use to cover the bathroom floor. Write the side lengths (in feet) of the square tiles.

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Interpret confidence intervals for population means

Full solution

Q. Problem

2

\newline

Tiles. A restaurant owner is replacing the restaurant's bathroom floor with square tiles. The tiles will be laid side-by-side to cover the entire bathroom with no gaps, and none of the tiles can be cut. The floor is a rectangle that measures

24

feet by

18

feet.

\newline

a. What is the largest possible tile size she could use? Write the side length in feet. Explain how you know it's the largest possible tile.

\newline

b. How many of these largest size tiles are needed?

\newline

c. Name more tile sizes that are whole number of feet that she could use to cover the bathroom floor. Write the side lengths (in feet) of the square tiles.

Calculate GCD: To find the largest tile size, we need the greatest common divisor (GCD) of the length and width of the floor. $\newline$ GCD of $24$ and $18$ is $6$ .
Determine Largest Tile Size: The largest possible tile size is $6$ feet by $6$ feet.
Calculate Number of Tiles: Now, to find out how many $6\times6$ tiles are needed, we divide the area of the floor by the area of one tile. $\newline$ The area of the floor is $24 \, \text{ft} \times 18 \, \text{ft} = 432 \, \text{sq ft}.$
Calculate Area of Floor: The area of one tile is $6 \, \text{ft} \times 6 \, \text{ft} = 36 \, \text{sq ft}.$
Calculate Area of One Tile: Dividing the total area by the area of one tile gives us $432 \, \text{sq ft} / 36 \, \text{sq ft}$ per tile $= 12$ tiles.
Consider Other Tile Sizes: For other whole number tile sizes, we need other divisors of both $24$ and $18$ . These include $1\times1$ , $2\times2$ , $3\times3$ , and $6\times6$ feet tiles.

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