Solved on Sep 26, 2023

Find the side length of the largest square tile that can cover a $15 \mathrm{in}$ . high and $24 \mathrm{in}$ . rectangular wall, where the tile side length must divide both height and width.

STEP 1

Assumptions1. The wall is a rectangle that is16 in. high and28 in. long. . Each square tile will have whole-number side lengths.
3. The side length of the tile must divide both16 in. and28 in.

STEP 2

First, we need to find the greatest common factor (GCF) of the height and length of the wall. The GCF will be the side length of the largest square tile that Kennedy can use.
To find the GCF, we first list the factors of each number.

STEP 3

List the factors of161,2,,8,16

STEP 4

List the factors of281,2,4,7,14,28

STEP 5

The common factors of16 and28 are1,2, and4. The greatest common factor is4.
Therefore, the side length of the largest square tile that Kennedy can use is4 in.

STEP 6

Now, we need to find out how many tiles Kennedy needs to completely fill the wall. We can do this by dividing the area of the wall by the area of a tile.
The area of the wall is the height of the wall multiplied by the length of the wall.
$Area_{wall} = Height_{wall} \\times Length_{wall}$

STEP 7

Plug in the values for the height and length of the wall to calculate the area of the wall.
$Area_{wall} =16\, in. \\times28\, in. =448\, in.^2$

STEP 8

The area of a tile is the side length of the tile squared.
$Area_{tile} = Side_{tile}^2$

STEP 9

Plug in the value for the side length of the tile to calculate the area of a tile.
$Area_{tile} =4\, in.^2 =16\, in.^2$

STEP 10

Now, divide the area of the wall by the area of a tile to find out how many tiles Kennedy needs.
$Number_{tiles} = Area_{wall} / Area_{tile}$

STEP 11

Plug in the values for the area of the wall and the area of a tile to calculate the number of tiles.
Number_{tiles} =448\, in.^ /16\, in.^

STEP 12

Calculate the number of tiles Kennedy needs.
$Number_{tiles} =448\, in.^2 /16\, in.^2 =28\, tiles$ Kennedy needs28 tiles to completely fill the wall.

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Find the side length of the largest square tile that can cover a $15 \mathrm{in}$ . high and $24 \mathrm{in}$ . rectangular wall, where the tile side length must divide both height and width.

STEP 1

Assumptions1. The wall is a rectangle that is16 in. high and28 in. long. . Each square tile will have whole-number side lengths.
3. The side length of the tile must divide both16 in. and28 in.

STEP 2

First, we need to find the greatest common factor (GCF) of the height and length of the wall. The GCF will be the side length of the largest square tile that Kennedy can use.
To find the GCF, we first list the factors of each number.

STEP 3

List the factors of161,2,,8,16

STEP 4

List the factors of281,2,4,7,14,28

STEP 5

The common factors of16 and28 are1,2, and4. The greatest common factor is4.
Therefore, the side length of the largest square tile that Kennedy can use is4 in.

STEP 6

Now, we need to find out how many tiles Kennedy needs to completely fill the wall. We can do this by dividing the area of the wall by the area of a tile.
The area of the wall is the height of the wall multiplied by the length of the wall.
$Area_{wall} = Height_{wall} \\times Length_{wall}$

STEP 7

Plug in the values for the height and length of the wall to calculate the area of the wall.
$Area_{wall} =16\, in. \\times28\, in. =448\, in.^2$

STEP 8

The area of a tile is the side length of the tile squared.
$Area_{tile} = Side_{tile}^2$

STEP 9

Plug in the value for the side length of the tile to calculate the area of a tile.
$Area_{tile} =4\, in.^2 =16\, in.^2$

STEP 10

Now, divide the area of the wall by the area of a tile to find out how many tiles Kennedy needs.
$Number_{tiles} = Area_{wall} / Area_{tile}$

STEP 11

Plug in the values for the area of the wall and the area of a tile to calculate the number of tiles.
Number_{tiles} =448\, in.^ /16\, in.^

STEP 12

Calculate the number of tiles Kennedy needs.
$Number_{tiles} =448\, in.^2 /16\, in.^2 =28\, tiles$ Kennedy needs28 tiles to completely fill the wall.

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Find the side length of the largest square tile that can cover a 15in15 \mathrm{in}15in. high and 24in24 \mathrm{in}24in. rectangular wall, where the tile side length must divide both height and width.

STEP 1

Assumptions1. The wall is a rectangle that is16 in. high and28 in. long. . Each square tile will have whole-number side lengths.3. The side length of the tile must divide both16 in. and28 in.

STEP 2

First, we need to find the greatest common factor (GCF) of the height and length of the wall. The GCF will be the side length of the largest square tile that Kennedy can use.To find the GCF, we first list the factors of each number.

STEP 3

List the factors of161,2,,8,16

STEP 4

List the factors of281,2,4,7,14,28

STEP 5

The common factors of16 and28 are1,2, and4. The greatest common factor is4.Therefore, the side length of the largest square tile that Kennedy can use is4 in.

STEP 6

STEP 7

Plug in the values for the height and length of the wall to calculate the area of the wall.Areawall=16 in.times28 in.=448 in.2Area_{wall} =16\, in. \\times28\, in. =448\, in.^2Areawall​=16in.times28in.=448in.2

STEP 8

The area of a tile is the side length of the tile squared.Areatile=Sidetile2Area_{tile} = Side_{tile}^2Areatile​=Sidetile2​

STEP 9

Plug in the value for the side length of the tile to calculate the area of a tile.Areatile=4 in.2=16 in.2Area_{tile} =4\, in.^2 =16\, in.^2Areatile​=4in.2=16in.2

STEP 10

Now, divide the area of the wall by the area of a tile to find out how many tiles Kennedy needs.Numbertiles=Areawall/AreatileNumber_{tiles} = Area_{wall} / Area_{tile}Numbertiles​=Areawall​/Areatile​

STEP 11

Plug in the values for the area of the wall and the area of a tile to calculate the number of tiles.Number_{tiles} =448\, in.^ /16\, in.^

STEP 12

Calculate the number of tiles Kennedy needs.Numbertiles=448 in.2/16 in.2=28 tilesNumber_{tiles} =448\, in.^2 /16\, in.^2 =28\, tilesNumbertiles​=448in.2/16in.2=28tilesKennedy needs28 tiles to completely fill the wall.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the side length of the largest square tile that can cover a $15 \mathrm{in}$ . high and $24 \mathrm{in}$ . rectangular wall, where the tile side length must divide both height and width.

Assumptions1. The wall is a rectangle that is16 in. high and28 in. long. . Each square tile will have whole-number side lengths.
3. The side length of the tile must divide both16 in. and28 in.

First, we need to find the greatest common factor (GCF) of the height and length of the wall. The GCF will be the side length of the largest square tile that Kennedy can use.
To find the GCF, we first list the factors of each number.

The common factors of16 and28 are1,2, and4. The greatest common factor is4.
Therefore, the side length of the largest square tile that Kennedy can use is4 in.

Plug in the values for the height and length of the wall to calculate the area of the wall.
$Area_{wall} =16\, in. \\times28\, in. =448\, in.^2$

The area of a tile is the side length of the tile squared.
$Area_{tile} = Side_{tile}^2$

Plug in the value for the side length of the tile to calculate the area of a tile.
$Area_{tile} =4\, in.^2 =16\, in.^2$

Now, divide the area of the wall by the area of a tile to find out how many tiles Kennedy needs.
$Number_{tiles} = Area_{wall} / Area_{tile}$

Plug in the values for the area of the wall and the area of a tile to calculate the number of tiles.
Number_{tiles} =448\, in.^ /16\, in.^

Calculate the number of tiles Kennedy needs.
$Number_{tiles} =448\, in.^2 /16\, in.^2 =28\, tiles$ Kennedy needs28 tiles to completely fill the wall.