The length of a persons shadow is proportional to their height. If a persons 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?

Rationale

The shadow of a person who is 135 cm tall is 90 cm long.

To determine the length of the shadow based on the proportional relationship between height and shadow length, we can set up a ratio using the measurements provided. Given that a person who is 180 cm tall casts a shadow of 120 cm, we can calculate the corresponding shadow length for a 135 cm tall person.

A (202.5 cm) YOUR ANSWER

This option represents an incorrect application of the proportional relationship. If the shadow were 202.5 cm, the ratio of height to shadow length would not hold true based on the original measurements provided, resulting in an unrealistic and inconsistent shadow length.

B (90 cm) CORRECT

Using the ratio from the initial values, the calculation follows: (135 cm / 180 cm) = (shadow length / 120 cm). Solving this gives a shadow length of 90 cm, accurately reflecting the proportional relationship. Therefore, this choice is indeed correct.

C (75 cm) YOUR ANSWER

This choice suggests a shorter shadow length than expected based on the established ratio. A height of 135 cm should correspond to a longer shadow than this option implies, thus violating the proportional relationship established by the original measurements.

D (160 cm) YOUR ANSWER

A shadow length of 160 cm would imply a person taller than 180 cm based on the consistent ratio. This choice does not correctly reflect the relationship since a shorter height should yield a shorter shadow length, making this option incorrect.

Conclusion

The relationship between a person's height and the length of their shadow is directly proportional. By applying this proportionality to the given heights and shadow lengths, we find that a person who is 135 cm tall would cast a shadow of 90 cm, maintaining the integrity of the original ratio established by the 180 cm tall person. This demonstrates the consistency of proportional relationships in real-world scenarios.

The length of a persons shadow is proportional to their height. If a persons 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?

The shadow of a person who is 135 cm tall is 90 cm long.

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