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 1/6 yd and width 1/6 yd. what is the ratio of the length of the tile to the length of the board? what is the ratio of the area of the title to the area of the board
(1/3 ft)/ (1/6 yd)
but, since 1 yd = 3 ft, you have
= (1/3 ft) / (1/2 ft)
= (1/3) / (1/2)
= 2/3
To find the ratios, we need to first convert the measurements to the same unit of measurement.
Given:
Tile length = 1/3 ft
Tile width = 1/3 ft
Board length = 1/6 yd
Board width = 1/6 yd
To find the ratio of the length of the tile to the length of the board, we need to convert the board length to feet:
1 yard = 3 feet
Therefore, 1/6 yd = (1/6) * 3 ft = 1/2 ft
Now we can calculate the ratio:
Length of the tile = 1/3 ft
Length of the board = 1/2 ft
Ratio of tile length to board length = (1/3 ft) / (1/2 ft) = (1/3) * (2/1) = 2/3
The ratio of the tile length to the board length is 2/3.
To find the ratio of the area of the tile to the area of the board, we need to convert the board measurements to square feet:
Board length = 1/2 ft
Board width = 1/2 ft
Now we can calculate the area:
Area of the tile = (1/3 ft) * (1/3 ft) = 1/9 square feet
Area of the board = (1/2 ft) * (1/2 ft) = 1/4 square feet
Ratio of tile area to board area = (1/9 square feet) / (1/4 square feet) = (1/9) * (4/1) = 4/9
The ratio of the area of the tile to the area of the board is 4/9.