Final answer:
A scale factor is used to represent the ratio between the scale model or drawing and the actual object. To determine actual dimensions from a scale drawing, multiply the model's dimensions by the inverse of the scale factor. For example, with a scale factor of 1/36 for a boat model, a 24-foot actual length translates to an 8-inch model.
Step-by-step explanation:
Scale drawings and models are representations of actual objects or places that are too big or too small to easily build or draw at full size. In mathematics, especially in geometry, scale factor is a very important concept that helps in creating these models or drawings accurately. When dealing with scale factors, we need to comprehend the ratio of the scale drawing to the actual object.
Applying Scale Factor to Find Measurements:
To find out the actual dimensions or lengths when given a scale factor, you simply need to multiply the measurements of the model or the drawing by the inverse of the given scale factor. For instance, if the scale factor of a drawing is 1/200, to find the actual length, you would multiply the length of the drawing by 200.
Here are examples of how to apply the concept of scale factor:
- If a boat model uses a scale factor of 1/36, and the actual boat is 24 feet long, the model should be 24 feet divided by 36, which is equal to 8 inches long (where 1 foot equals 12 inches).
- For a drawing with a scale factor of 1/150, such as Anna's house diagram, the distance on the diagram would be calculated by dividing the actual distance by the factor. So, the distance from the room to the kitchen being 15 meters would be represented as 15 meters divided by 150, which is 0.1 meters or 10 centimeters on the diagram.
- Similarly, for a scale model of a height of a doghouse intended to be 6 feet tall using a scale of 1/24, you'd divide the actual height by the scale factor to get the model height. So, 6 feet divided by 24 gives us a model that is 0.25 feet tall, or 3 inches.