an artist is using tiles and boards for a project. a tile has length 1/3 ft and width 1/3 ft a board has length 1/2 yd and width 1/2 yd. what is the ratio of the tile to the length of the board? What is the area of the tile to the length of the board? what is the area of the tile to the area of the board?

1

tile : board = 1/3 ft : 1/2 yds

= 4 inches : 18 inches
= 2 : 9

area of tile : area of board = 2^2 : 9^2 = 4 : 81

well your all right

To find the ratio of the tile to the length of the board, we need to convert the units of measurement to a common unit.

The length of the tile is given as 1/3 ft and the length of the board is given as 1/2 yd. We can convert the length of the tile to yards as follows:

1 ft = 1/3 yd

So, 1/3 ft = (1/3) * (1/3) yd = 1/9 yd

Now, the ratio of the tile to the length of the board is:

1/9 yd / 1/2 yd = (1/9) * (2/1) = 2/9

Therefore, the ratio of the tile to the length of the board is 2/9.

To find the area of the tile to the length of the board, we need to calculate the areas of the tile and the board first.

The area of the tile is the product of its length and width:

Area of tile = (1/3 ft) * (1/3 ft) = 1/9 square ft

Now, we convert the length and width of the board to feet:

1 yd = 3 ft

So, the length of the board is:

1/2 yd = (1/2) * (3/1) ft = 3/2 ft

The width of the board is also 3/2 ft.

The area of the board is the product of its length and width:

Area of board = (3/2 ft) * (3/2 ft) = 9/4 square ft

Therefore, the ratio of the area of the tile to the length of the board is:

(1/9 square ft) / (3/2 ft) = (1/9) * (2/3) = 2/27

Therefore, the ratio of the area of the tile to the length of the board is 2/27.

Next, to find the area of the tile to the area of the board, we simply divide the area of the tile by the area of the board:

Area of tile / Area of board = (1/9 square ft) / (9/4 square ft) = (1/9) * (4/9) = 4/81

Therefore, the ratio of the area of the tile to the area of the board is 4/81.