QuestionFind the smallest square size for $18 \mathrm{~cm}$ by $24 \mathrm{~cm}$ tiles. Can they cover a $6.48 \mathrm{~m}$ by $15.12 \mathrm{~m}$ floor?

Studdy Solution

STEP 1

Assumptions1. The dimensions of the tile are18 cm by24 cm. The tiles cannot be cut3. The smallest square that can be tiled using the given tile is sought4. The dimensions of the floor are6.48 m by15.12 m5. We are checking if the tiles can be used to cover the entire floor without any leftover space

STEP 2

First, we need to find the greatest common divisor (GCD) of the dimensions of the tile. This will give us the side length of the smallest square that can be tiled using the given tile.
$GCD = GCD(18,24)$

STEP 3

Calculate the greatest common divisor (GCD) of18 and24.
$GCD =6$

STEP 4

The side length of the smallest square that can be tiled using the given tile is6 cm. So, the dimensions of the smallest square are6 cm by6 cm.
Now, let's move on to part b of the problem.

STEP 5

First, we need to convert the dimensions of the floor from meters to centimeters because the dimensions of the tiles are given in centimeters.
$Length =.48 m =648 cm$ $Width =15.12 m =1512 cm$

STEP 6

Next, we need to check if the length and width of the floor are divisible by the side length of the smallest square that can be tiled using the given tile.
$Length\, divisible =648 \mod6 =0$ $Width\, divisible =1512 \mod6 =0$

STEP 7

Calculate the remainder when the length and width of the floor are divided by the side length of the smallest square.
$Length\, remainder =648 \mod6 =0$ $Width\, remainder =1512 \mod6 =0$ Since both remainders are0, the tiles can be used to cover the entire floor without any leftover space.

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QuestionFind the smallest square size for $18 \mathrm{~cm}$ by $24 \mathrm{~cm}$ tiles. Can they cover a $6.48 \mathrm{~m}$ by $15.12 \mathrm{~m}$ floor?

Studdy Solution

STEP 1

Assumptions1. The dimensions of the tile are18 cm by24 cm. The tiles cannot be cut3. The smallest square that can be tiled using the given tile is sought4. The dimensions of the floor are6.48 m by15.12 m5. We are checking if the tiles can be used to cover the entire floor without any leftover space

STEP 2

First, we need to find the greatest common divisor (GCD) of the dimensions of the tile. This will give us the side length of the smallest square that can be tiled using the given tile.
$GCD = GCD(18,24)$

STEP 3

Calculate the greatest common divisor (GCD) of18 and24.
$GCD =6$

STEP 4

The side length of the smallest square that can be tiled using the given tile is6 cm. So, the dimensions of the smallest square are6 cm by6 cm.
Now, let's move on to part b of the problem.

STEP 5

First, we need to convert the dimensions of the floor from meters to centimeters because the dimensions of the tiles are given in centimeters.
$Length =.48 m =648 cm$ $Width =15.12 m =1512 cm$

STEP 6

Next, we need to check if the length and width of the floor are divisible by the side length of the smallest square that can be tiled using the given tile.
$Length\, divisible =648 \mod6 =0$ $Width\, divisible =1512 \mod6 =0$

STEP 7

Calculate the remainder when the length and width of the floor are divided by the side length of the smallest square.
$Length\, remainder =648 \mod6 =0$ $Width\, remainder =1512 \mod6 =0$ Since both remainders are0, the tiles can be used to cover the entire floor without any leftover space.

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QuestionFind the smallest square size for 18 cm18 \mathrm{~cm}18 cm by 24 cm24 \mathrm{~cm}24 cm tiles. Can they cover a 6.48 m6.48 \mathrm{~m}6.48 m by 15.12 m15.12 \mathrm{~m}15.12 m floor?

Studdy Solution

STEP 1

Assumptions1. The dimensions of the tile are18 cm by24 cm. The tiles cannot be cut3. The smallest square that can be tiled using the given tile is sought4. The dimensions of the floor are6.48 m by15.12 m5. We are checking if the tiles can be used to cover the entire floor without any leftover space

STEP 2

First, we need to find the greatest common divisor (GCD) of the dimensions of the tile. This will give us the side length of the smallest square that can be tiled using the given tile.GCD=GCD(18,24)GCD = GCD(18,24)GCD=GCD(18,24)

STEP 3

Calculate the greatest common divisor (GCD) of18 and24.GCD=6GCD =6GCD=6

STEP 4

The side length of the smallest square that can be tiled using the given tile is6 cm. So, the dimensions of the smallest square are6 cm by6 cm.Now, let's move on to part b of the problem.

STEP 5

First, we need to convert the dimensions of the floor from meters to centimeters because the dimensions of the tiles are given in centimeters.Length=.48m=648cmLength =.48 m =648 cmLength=.48m=648cmWidth=15.12m=1512cmWidth =15.12 m =1512 cmWidth=15.12m=1512cm

STEP 6

STEP 7

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QuestionFind the smallest square size for $18 \mathrm{~cm}$ by $24 \mathrm{~cm}$ tiles. Can they cover a $6.48 \mathrm{~m}$ by $15.12 \mathrm{~m}$ floor?

First, we need to find the greatest common divisor (GCD) of the dimensions of the tile. This will give us the side length of the smallest square that can be tiled using the given tile.
$GCD = GCD(18,24)$

Calculate the greatest common divisor (GCD) of18 and24.
$GCD =6$

The side length of the smallest square that can be tiled using the given tile is6 cm. So, the dimensions of the smallest square are6 cm by6 cm.
Now, let's move on to part b of the problem.

First, we need to convert the dimensions of the floor from meters to centimeters because the dimensions of the tiles are given in centimeters.
$Length =.48 m =648 cm$ $Width =15.12 m =1512 cm$