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 1/2 in and width 1/6 in. The actual tiles have length 2/3 ft and width 2/9 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? Use pencil and paper. Describe two ways to find each ratio.

Answer 1

The ratio of the lengths of tiles in the model to actual tiles is 1:16, and the ratio of their areas is 1:128. These ratios can be found through direct comparison or by calculating and comparing areas, after unit conversion if needed.

Step-by-step explanation:

The ratio of the length of a tile in the model to the length of an actual tile is found by comparing the two lengths directly. Since the model tile has a length of 1/2 inch and the actual tile has a length of 2/3 foot (which is 8 inches, because there are 12 inches in a foot), the ratio is 1/2 inch to 8 inches, or 1:16 when simplified.

To find the ratio of the area of a tile in the model to the area of an actual tile, we need to calculate the area of each and then compare. The area of the model tile is (1/2 inch) x (1/6 inch) = 1/12 square inches. The area of the actual tile is (2/3 foot x 12 inches/foot) x (2/9 foot x 12 inches/foot) = 32/3 square inches. So the ratio of the areas is (1/12 square inches) to (32/3 square inches), which simplifies to 1:128.

There are two methods to find each ratio: direct comparison of the lengths and widths, converting units if necessary; and calculation of area followed by comparison of those areas.