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 ½ in. and width ⅙ in. The actual tiles have length ⅓ ft and width one-ninth 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? Use pencil and paper. Describe two ways to find each ratio. The ratio of the length of a tile in the model to the length of an actual tile is (Type the ratio as a simplified fraction.) Enter your answer in the answer box and then click Check Answer.

Option 1: 1/18
Option 2: 1/3
Option 3: 3/2
Option 4: 9/2

Answer 1

The ratio of the length of a tile in the model to the length of an actual tile is 1/18.

Step-by-step explanation:

To find the ratio of the length of a tile in the model to the length of an actual tile, we can compare the scale distance to the actual distance. In the model, each tile has a length of 1/2 inch, while in real life, the tiles have a length of 1/3 feet.

We can set up a proportion to find the ratio: (1/2 inch) / (1/3 feet) = x / 1 feet. To solve for x, we cross multiply and divide: x = (1/2) * (1/3) = 1/6 feet.

Therefore, the ratio of the length of a tile in the model to the length of an actual tile is 1/6 feet, which is equivalent to the simplified fraction 1/18. Option 1: 1/18 is the correct answer.