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 = [tex]\frac{1}{3} \cdot 0.33= 0.11[/tex] yd
The width of the tile = [tex]\frac{1}{3} \cdot 0.33= 0.11[/tex] yd
Hence, the ratio of length of the tile to the length of the board is given by
[tex]\frac{0.11}{1/4} \\
\\
\frac{44}{100} \\
\\
\frac{11}{25} \\[/tex]
Area of tile = [tex]0.11 \times 0.11 = 0.0121[/tex] square yd.
Area of board is [tex]\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}[/tex]
Therefore, the ratio of the area of the tile to the area of the board is given by
[tex]\frac{0.0121}{1/16} \\
\\
\frac{121}{625}[/tex]
