Final answer:
The problems involve calculating scale model dimensions using a given scale factor. By setting up a proportional relationship between the model and actual dimensions, students can find the scaled dimensions for height, width, and length, as well as map distances.
Step-by-step explanation:
The student asked about using a scale factor to convert measurements of a real-world object to a scale model and vice versa. The concept involves setting up a proportional relationship between the dimensions in the scale model and the real dimensions. This type of problem is commonly found in geometry and measurement units within mathematics curriculum, typically at the high school level.
Step-by-Step Examples:
1. To find the height of Haley's school building in her scale model, we would set up a proportion using the scale 1 inch = 6 feet. Since the actual height is 30 feet, we divide 30 feet by 6 to find the height in her model, which is 5 inches.
2. For the width of Haley's school, which is 120 feet, in the scale model, we would again use the scale 1 inch = 6 feet. Dividing 120 feet by 6 gives us 20 inches, which would be the width in her scale model.
3. Using the same scale, to find the length of Haley's school in the scale model, we'd divide 180 feet (actual length) by 6, resulting in a scale model length of 30 inches.
Eddie's Map Problem:
Using the scale 1 centimeter = 8 meters, for the distance between the post office and City Hall on Eddie's map, we would convert the actual distance of 56 meters to the distance on the map by dividing 56 meters by 8, yielding a distance of 7 centimeters on the map.