Final answer:
In problems involving scale factors, proportions are used to find missing dimensions. A scale factor of 1:4 implies that the original dimension is four times the size of the scaled dimension. By applying this to different scenarios, one can find the base of an original shape, the scale of a drawing, or the size of a model.
Step-by-step explanation:
To solve problems involving scale factors, we'll use proportions to determine the missing dimensions. The scale factor describes how much the original dimensions are increased or decreased.
Using Scale Factor for Proportions
Given that the scale factor is 1:4, we can create a proportion to solve for the missing dimension of a shape. For example, with a scale measurement of 4 and a scale factor of 1:4, the proportion is set up as:
1/4 = 4/x
By cross-multiplying to solve for x, we see that x (the original dimension) is 16, meaning the base of the original triangle is 16 when the reduced base is 4.
Examples Involving Scale Factors
- If you have a rectangle with a width that has to be scaled down from 9 inches to 2 inches, the scale factor would be 2/9.
- For a man who is 64 inches tall, represented in a drawing by 4 inches, the scale factor would be 4/64 or 1/16.
- Considering a model boat that is 24 feet in actual size with a scale factor of 1/36, the model should be 8 inches long (since there are 12 inches in a foot, 24 feet is 288 inches, and 288 inches divided by 36 is 8 inches).