34. The length of a person's shadow is proportional to their height. If a person's shadow is 120 cm long and their height is 180 cm, how long is the shadow of a person who is 135 cm tall at the same time of day?
Answer: D
The shadow of a person who is 135 cm tall is 90 cm long.
To find the length of the shadow of a person who is 135 cm tall, we can use the proportional relationship between height and shadow length established by the given measurements. Since the original person's height is 180 cm and their shadow is 120 cm, we can set up a proportion to determine the new shadow length.
A) 202.5 cm
This option is incorrect because it suggests that the shadow length increases disproportionately compared to the height of the person. If we apply the proportional relationship, 202.5 cm would imply an unreasonable shadow length that does not maintain the established ratio.
B) 75 cm
While this option might seem plausible, it underestimates the length of the shadow based on the height of the person. The proportional relationship shows that for a height of 135 cm, the shadow must be longer than 75 cm to maintain consistency with the original proportions.
C) 160 cm
This option is also incorrect as it suggests a shadow length that exceeds the original measurements. If the shadow were 160 cm, it would imply a height of more than 180 cm in relation to the original measurements, which contradicts the established proportional relationship.
D) 90 cm
This is the correct option. By using the proportional relationship, we calculate the new shadow length for a height of 135 cm, which results in a shadow of 90 cm. This aligns with the original ratio of height to shadow length.
Conclusion
The correct answer, 90 cm, follows the established proportional relationship between height and shadow length. All other options fail to accurately represent the relationship, either overestimating or underestimating the expected shadow length based on the given height. Thus, 90 cm is the only reasonable conclusion based on the provided data.