Calculating the Room Width Using Tiles

When it comes to calculating the width of a room using square tiles, we often need to know specific dimensions and quantities. In this case, we are provided with a length of the floor and the dimensions of the tiles. Let's break down the problem and find the width of the room without any cuts in the tiles.

Understanding the Tiles and Dimensions

The tiles in question are square, each measuring 30 cm x 30 cm. The length of the floor of the room is 7 m 20 cm. This needs to be converted to centimeters for easier calculations. Therefore, the length of the room is 720 cm (since 1 meter 100 cm).

Calculating the Number of Tiles for the Length

We are informed that it takes 24 tiles to cover the length of 720 cm exactly. This gives us a clear indication of the arrangement of the tiles along the length of the room. Each tile is 30 cm, so if 24 tiles fit the length, the calculation is straightforward:

Number of tiles for length Length of the room / Length of one tile
Number of tiles for length 720 cm / 30 cm
Number of tiles for length 24

Determining the Width of the Room

To find the width of the room, we need to use the same logic. Since no tiles are cut, the width must be a multiple of the tile's length. Let's denote the width of the room as ( W ) cm, and it must be a multiple of 30 cm.

The total area of the room can be calculated by multiplying the length and width:

Area of the room Length of the room x Width of the room
Area of the room 720 cm x W cm

The area can also be determined by the number of tiles used for both length and width. If 24 tiles fit the length, the width ( W ) must fit a whole number of 30 cm tiles. Since the problem does not specify the number of tiles used for the width, we can determine ( W ) by ensuring that the width is a multiple of 30 cm.

A common and practical width for a room, ensuring no tile is cut, would be 30 cm, 60 cm, 90 cm, 120 cm, etc. However, without additional information, we cannot pinpoint the exact width. To find it, we need to know the number of tiles that fit the width.

Conclusion

In summary, the width of the room must be a multiple of 30 cm. With the given information, we can determine the width based on the number of tiles used for the width. For instance, if it takes 8 tiles to cover the width, the width would be 240 cm (as 8 x 30 cm 240 cm).

Key Takeaways:

The given problem requires the width to be a multiple of the tile's dimension, which is 30 cm. No specific width is provided without knowing the number of tiles for the width. The width of the room is dependent on the number of tiles used for both length and width.

Related Keywords: room width calculation, tile dimensions, floor coverage