Final answer:
To answer the schoolwork question involving the determination of missing sides and the value of X, a scale factor is used. A proportion based on the scale model is set up to solve for the actual dimensions, using multiplication and division. The provided examples illustrate how to find actual dimensions when given different scale factors.
Step-by-step explanation:
To determine the missing sides and what X equals, we should first establish the scale factor for the dimensions of the square. The dimensions of the larger square are twice that of the first square, making the scale factor 2. This means the side length of the larger square is 8 inches (4 inches x 2).
Next, we set up a proportion to find the missing length represented as X. We have a scale length of 8 inches, so we write the ratio as 0.5 inch/20 miles = 8 inches/X miles. To solve for X, cross-multiply and divide to get the actual length in miles that corresponds to 8 inches on the scale model.
Finally, to find the actual dimension if the scale factor is given, like 1/4":4' (as in example 4.8.4.3), you would write the proportion and solve for the actual dimension. Similar steps are followed in example 4.8.4.2 where the scale factor is 2":3' and the scale measurement is 6 inches.