Question

An architect makes a model of a new house. The model shows a tile patio in the back yard. in the model, each has length 1/2 in. and width 1/4 in. The actual rules have length 1/4 ft and width 3/16 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? Describe two ways to find each ratio.​

Answer 1

To determine the ratios of length and area of a tile in the model to the actual tile, divide the model tile's size by the actual tile's size. The ratio of the lengths is 1/6, and the ratio of the areas is 1/54 after converting all measurements to a common unit, inches.

Step-by-step explanation:

The question asks to determine the ratio of the length and the area of a tile in a model to the actual tile. To find the ratio of the length of a tile in the model to the actual tile, one must simply divide the length of a model tile by the length of an actual tile. The length of a model tile is given as 1/2 inch, and the actual tile's length is 1/4 foot. We convert 1/4 foot to inches by multiplying by 12 (since there are 12 inches in a foot), which gives us 3 inches. Hence, the ratio of the lengths is (1/2) inch / 3 inches = 1/6.

To find the area ratios, the area of each tile must be calculated in their respective units and then compared. The area of a model tile is (1/2 inch) × (1/4 inch) = 1/8 square inches. To find the area of the actual tile, we first convert the dimensions to inches: 1/4 foot is 3 inches, and 3/16 foot is 3/16 × 12 inches = 2.25 inches. So, the actual tile's area is 3 inches × 2.25 inches = 6.75 square inches. The ratio of the areas is then 1/8 square inches / 6.75 square inches = 1/54.

There are two ways to find these ratios: first, by direct division as shown, and second, by converting all measurements to a common unit (such as inches) before computing the ratios.