An artist is using tiles and boards for a project. A tile has a length of 2/3 ft and width 2/3 ft. A board has a length of 1/2 yd and a width of 1/2 yd. What is the ratio of the length of the tile is the length of the board? What is the ratio of the area of the tile to the area of the board?
I've tried SO many times to answer this question, but I'm so stuck! Help, please!!
1 yard = 3 ft
so ratio of tile to board
= (2/3) : 3
= 2 : 9
area of board = 3 ft by 3 ft
= 9 square feet
area of tile = (2/3)(2/3) = 4/9
ratio of area of tile : area of board
= (4/9) : 9
= 4 : 81
No worries, I can help you out with this problem!
To find the ratio of the length of the tile to the length of the board, we need to convert the measurements to the same units. Let's convert the tile length from feet to yards:
1 yard = 3 feet
Since the tile length is 2/3 feet, we can divide it by 3 to get the length in yards:
(2/3) ft ÷ 3 = 2/9 yds
So, the ratio of the length of the tile to the length of the board is 2/9.
Now, let's find the ratio of the area of the tile to the area of the board. To do this, we need to calculate the areas of both the tile and the board.
The area of the tile can be found by multiplying its length and width:
Area of tile = (2/3 ft) * (2/3 ft) = (4/9) ft^2
The area of the board can be found by multiplying its length and width as well:
1 yard = 3 feet
Length of board = (1/2) yd = (1/2) * 3 ft = 3/2 ft
Width of board = (1/2) yd = (1/2) * 3 ft = 3/2 ft
Area of board = (3/2 ft) * (3/2 ft) = (9/4) ft^2
Now, let's find the ratio of the areas:
Area of tile ÷ Area of board
= (4/9 ft^2) ÷ (9/4 ft^2)
= (4/9 ft^2) * (4/9 ft^2) {flip the denominator and multiply}
= 16/81
So, the ratio of the area of the tile to the area of the board is 16/81.
I hope this helps! Let me know if you have any further questions.