Question

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?

Answer 1

Ratio of lengths is 1:3

Ratio of areas is 1:9

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