Question

An architect makes a model of a new house. The model shows a tile patio in the backyard. In the​ model, each tile has length 1/4 in. and width 1/6 in. The actual tiles have length 1/6 ft and width 1/9 ft.

What is the ratio of the length of a tile in the model to the length of an actual​ tile? What is the ratio of the area of a tile in the model to the area of an actual​ tile

Answer 1

The answer is below

Explanation:

The model is a tile with length 1/4 in. and width 1/6 in while the actual tile has length 1/6 ft. and width 1/9 ft.

Firstly we have to convert the model length and width from inches to feet.

1 feet = 12 inches

model length = 1/4 in. = 1/4 in * (1/12) ft./in = 1/48 ft.

model width = 1/6 in. = 1/6 in * (1/12) ft./in = 1/72 ft.

Therefore:

Ratio of model length to actual length of tile = (1/48 ft.) / (1/6 ft.) = 1 / 8

Ratio of model length to actual length of tile = (1/72 ft.) / (1/9 ft.) = 1 / 8

Area of model tile = length * width = 1/48 ft. * 1/72 ft. = 1/3456 ft²

Area of actual tile = length * width = 1/6 ft. * 1/9 ft. = 1/54 ft²

Ratio of model area to actual area of tile = (1/3456 ft²) / (1/54 ft²) = 1 / 64