Question

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 1/4yd and width 1/4 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 tile to the area of the​ board?

Answer 1

We have been given that

The length of the tile is given by 1/3 feet.

The width of the tile is given by 1/3 feet.

The length of the board is given by 1/4 yd.

The width of the board is given by 1/4 yd.

We know that 1 feet = 0.33 yard

Hence, we have

The length of the tile =  $\frac{1}{3} \cdot 0.33= 0.11$ yd

The width of the tile =  $\frac{1}{3} \cdot 0.33= 0.11$ yd

Hence, the ratio of length of the tile to the length of the​ board is given by

$\frac{0.11}{1/4} \\ \\ \frac{44}{100} \\ \\ \frac{11}{25}$

Area of tile = $0.11 \times 0.11 = 0.0121$ square yd.

Area of board is $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$

Therefore, the ratio of the area of the tile to the area of the​ board is given by

$\frac{0.0121}{1/16} \\ \\ \frac{121}{625}$