13. Television screen sizes are measured by the diagonal length of the rectangular screen. Assuming proportionality, if a vehicle on a 32-inch screen appears 9 inches long, how long will it appear on a 50-inch screen? (Round to the nearest inch.)
Answer: C
The vehicle will appear 15 inches long on a 50-inch screen.
Using proportionality, we can determine the size of the vehicle on a larger screen. The ratio of the vehicle's size on the two screens can be calculated based on their diagonal lengths.
A) 27 in
This option suggests that the vehicle would appear 27 inches long on the 50-inch screen. However, this is incorrect as it significantly overestimates the proportional increase based on the screen size ratio.
B) 18 in
While this option is a plausible length, it does not correctly apply the proportional relationship between the screen sizes. The calculation shows that this would also be an overestimate of the vehicle's size on the larger screen.
C) 15 in
This is the correct answer. By applying the proportionality rule, we find that if the 32-inch screen shows the vehicle at 9 inches, scaling up to a 50-inch screen leads to a vehicle size of 15 inches, maintaining the same aspect ratio.
D) 11 in
This option underestimates the size of the vehicle on the 50-inch screen. The calculation demonstrates that the proportional relationship would yield a larger size than 11 inches, making this option incorrect.
Conclusion
The correct answer is 15 inches, which accurately reflects the proportional scaling of the vehicle's size from a 32-inch screen to a 50-inch screen. Other options either overestimate or underestimate the size based on the given ratios, failing to adhere to the principle of proportionality necessary for this calculation.