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 a length 1/2in and 1/6in. The actual tiles have length 2/3ft and 2/9ft. What is the ratio of the length of a tile in the model to the length of actual tile? What is the ratio of the area of tile in the model to the area of an actual tile?

Answer 1

Ratio of the lengths = 1 : 16 and 1 : 15.71

Ratio of the Area = 1 : 251.29

Explanation:

Model = 1/2in and 1/6in.

Actual = 2/3ft and 2/9ft.

1 ft = 12 inches

2/3 ft = 8 inches

2/9 ft = 2.67 inches

Model = 0.5 inches and 0.17 inches

Actual = 8 inches and 2.67 inches

Ratio

0.5 : 8 and 0.17 : 2.67

= 0.5 / 8 and 0.17 / 2.67

= 1 / 16 and 1 / 15.71

= 1 : 16 and 1 : 15.71

Area of the tile in the model = length × width

= (0.5 × 0.17) inches

= 0.085 inches

Area of the actual tile = length × width

= (8 × 2.67) inches

= 21.36 inches

Ratio of the area

0.085 : 21.36

= 0.085 / 21.36

= 1 : 251.29