Final answer:
To find the proportional side length for a scaled copy, we establish a ratio comparing scale to actual dimensions, set up proportions, and solve for the unknown dimension. Examples provided illustrate the process of setting these proportions and solving them to find missing dimensions in various scale factor scenarios.
Step-by-step explanation:
To determine the proportional side length for a scaled copy, we need to establish a ratio that compares the scale dimension to the actual dimension. When given two ratios, such as scale/actual=1/20 and scale/actual=1/5.5, our task is to set up equivalent proportions to solve for the unknown dimension.
Example 4.8.4.2 demonstrates this: to find the missing actual dimension with a scale factor of 2" to 3' and a scale measurement of 6", we can write the proportion 2"/3' = 6"/actual. By cross-multiplying and solving the proportion, we can find the actual dimension.
To apply this to our original problem, we need to know either the scale dimension or the actual dimension for Figure e or Figure f. Let's consider an example with the provided ratios. If we have a scale of 1/20 and need to find the equivalent scale when the actual is 5.5 times larger, we could write the proportion 1/20 = x/5.5, where x represents the unknown scaled dimension for the larger figure.
The same process applies when we set proportions for length and width. For instance, if the length has a unit scale of 1/50, and we have an actual length of 0.5 and a width of w, we can set up two proportions: Length = 1/50 = 0.5/actual length and Width = w/10 = 0.5/actual width. The steps to solve are: cross-multiply and solve each equation for the unknown actual dimensions.