Final answer:
To return a scaled copy to its original size, use the inverse of the original scale factor. For example, if the scale factor was 1/200, use 200. Set up a proportion to solve for either the scale or actual dimensions.
Step-by-step explanation:
If you have a scaled copy of an object and you want to return it to its original size, you need to use a scale factor that is the inverse of the scale factor used to create the scaled copy. For example, if a drawing was scaled down with a scale factor of 1/200, meaning the actual size is 200 times the drawing, to return it to its original size you would use a scale factor of 200. Similarly, if a model boat was built with a scale factor of 1/36, you would use a scale factor of 36 to get back to the actual size.
To solve problems involving scale dimensions or actual dimensions, you usually set up a proportion using the given scale factor. If the dimensions are to be scaled up or down, you multiply the scale dimensions by the scale factor to get the actual dimensions, and vice versa.
Example Problems
Madeline's model boat's actual length is 24 feet, and she used a scale factor of 1/36. The model length in inches would be 24 feet x 12 inches/foot x 1/36 = 8 inches.If a drawing of a box has dimensions that are 2 inches, 3 inches, and 5 inches and the actual box will be 3(1/4) times the dimensions in the drawing, the actual dimensions will be 6.5 inches, 9.75 inches, and 16.25 inches respectively.To find the scale factor when three inches is equal to twelve feet, we write the ratio as 3 inches/12 feet, which gives us a scale factor of 1/4 or 1:4 since there are 12 inches in a foot.