30. 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?
Answer: B
The shadow of a person who is 135 cm tall is 90 cm long.
The relationship between a person's height and the length of their shadow can be calculated using proportions. Given that a person with a height of 180 cm has a shadow of 120 cm, we can set up a proportion to find the shadow length of a 135 cm tall person.
A) 202.5 cm
Option A is incorrect because it suggests that the shadow length increases disproportionately with height. Using the proportion, the expected shadow length for a height of 135 cm is much shorter than this value.
B) 90 cm
Option B is the correct answer. The calculation is based on the ratio of height to shadow length: (120 cm shadow / 180 cm height) = (X cm shadow / 135 cm height). Solving for X gives a shadow length of 90 cm.
C) 75 cm
Option C is incorrect as it underestimates the shadow length based on the given proportions. The calculation shows that a 135 cm tall person would cast a longer shadow than 75 cm when compared to the original values.
D) 160 cm
Option D is also incorrect because it suggests an exaggerated shadow length. The height-to-shadow ratio would not support such a long shadow for a person of 135 cm.
Conclusion
Option B is definitively correct as it accurately reflects the proportional relationship between height and shadow length derived from the initial data. All other options fail to maintain the correct ratio, resulting in unrealistic shadow lengths for the given height.