Final answer:
To find the unknown side length 'x', we set up a proportion utilizing the provided scale lengths. By cross-multiplying and solving for 'x', we find that 'x' equals 6000 miles and 450 miles for the respective ratios. The answer options provided do not match these results, suggesting a potential error or missing context in the question.
Step-by-step explanation:
The question asks us to find the unknown side length, X, where the scale length is given, and we need to represent the proportion as a ratio. One of the provided ratios is 1 inch/2000 miles = 3 inches/x miles. To find the unknown length 'x', we can set up a proportion and solve for 'x'.
Using cross-multiplication, we get:
- 1 inch / 2000 miles = 3 inches / x miles
- 1 * x = 2000 * 3
- x = 6000 miles
Therefore, the unknown side length 'x' in miles, when the scale is 3 inches, is 6000 miles. When looking at another ratio given, 0.5 inches/75 miles = 3 inches/x miles, the same steps apply:
- 0.5 inches / 75 miles = 3 inches / x miles
- 0.5 * x = 75 * 3
- x = 450 miles
So, for the second ratio, the unknown side length 'x' in miles, when the scale is 3 inches, is 450 miles. Notably, the given answer choices in the question do not match these calculations, which could indicate the question is missing context or that there has been a misunderstanding.