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?

Rationale

The length of the shadow of a person who is 135 cm tall at the same time of day is 90 cm.

The relationship between a person's height and the length of their shadow is proportional, which means they increase or decrease at the same rate. Hence, if the shadow of a person with height 180 cm is 120 cm, the shadow length of a person with a height of 135 cm can be calculated by maintaining the same ratio of height to shadow length.

A (202.5 cm) YOUR ANSWER

This is incorrect. The relationship between a person's height and their shadow length is one of proportionality, not direct equality. Hence, the shadow length will not exceed the person's height, especially when considering the given ratio from the first person's height and shadow length.

B (75 cm) YOUR ANSWER

This is incorrect. While the shadow length is less than the person's height, it does not maintain the same proportionality established in the original scenario (180 cm height: 120 cm shadow). The correct shadow length must maintain this ratio.

C (160 cm) YOUR ANSWER

This is incorrect. The shadow length, in this case, is actually greater than the person's height, which contradicts the proportional relationship established between height and shadow length in the original scenario.

D (90 cm) CORRECT

This is the correct answer. The shadow length of 90 cm maintains the same proportionality with a height of 135 cm as the original scenario (180 cm height: 120 cm shadow).

Conclusion

The length of a person's shadow is proportional to their height. Thus, if a person's shadow is 120 cm long and their height is 180 cm, then the shadow of a person who is 135 cm tall at the same time of day will be 90 cm long, as this maintains the same ratio of height to shadow length. Incorrect answers fail to preserve this proportional relationship, either exceeding the person's height or not aligning with the given ratio.

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?

The length of the shadow of a person who is 135 cm tall at the same time of day is 90 cm.

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