Final answer:
The minimum width of the small box should be proportional to the larger box, at 0.9 times the length of the smaller mirror. Without the length of the smaller mirror, we cannot calculate an exact width, but it should follow the ratio of 0.9 that exists between the width and length of the larger mirror.
Step-by-step explanation:
The question involves finding the minimum width for a smaller box to fit a mirror that is similar in proportion to a larger mirror. Since the larger mirror fits in a box that is 18 inches wide by 20 inches long, we need to maintain the same proportion for the smaller mirror. Let's denote the width of the smaller mirror as 'w' and its corresponding length as 'l'. The proportion can be expressed by the ratio of width to length for both mirrors:
- Larger mirror: 18 inches wide / 20 inches long = 0.9
- Smaller mirror: w inches wide / l inches long = 0.9
To keep the proportion the same, the width of the smaller mirror should be 0.9 times its length. However, the question asks for the minimum width needed, so we do not have the value for the length. Still, whatever the length is, the width should be 0.9 times that to maintain the proportion.