An artist is using tiles and boards for a project. A tile has length 1/4 ft and width 1/4 ft. A board has length 1/4 yd 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?

Ratio of lengths is 1:3

Ratio of areas is 1:9

Step-by-step explanation:

Firstly, we need the units to be same

Mathematically, 1 yard = 3 feet

A length of 1/4 yards = 1/4 * 3 = 3/4 feet

A width of 1/4 yards = 1/4 * 3 = 3/4 feet

The ratio of the length of the tile to the length of the board

that would be;

1/4 : 3/4 = 1: 3

Let’s now work with area

Mathematically, area in both cases is length * width

For the board, we have that;

3/4 * 3/4 = 9/16 square feet

For the tile, we have that;

1/4 * 1/4 = 1/16 square feet

so the ratio of the tile area to the board area will be;

1/16 : 9/16 = 1: 9

answer:

c. the third graph