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A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time, a tower casts a shadow 40 m long on the ground. The height of the tower is
- a)72 m
- b)60 m
- c)65 m
- d)70 m
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At...
We can solve it through ratio proportion rule,
let the tower is x m long, then
12 cm stick casts → 8 cm shadow
x m tower casts → 40 m shadow
On cross multiplying, we get
Hence, option B is correct.
let the tower is x m long, then
12 cm stick casts → 8 cm shadow
x m tower casts → 40 m shadow
On cross multiplying, we get
Hence, option B is correct.
Most Upvoted Answer
A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At...
Understanding the Problem
To find the height of the tower based on the shadow lengths, we can use the concept of similar triangles. The ratio of the height of an object to the length of its shadow remains constant for both the stick and the tower since they are being illuminated by the same light source.
Given Data
- Height of the stick: 12 cm
- Length of the stick's shadow: 8 cm
- Length of the tower's shadow: 40 m (which is 4000 cm for consistent units)
Setting Up the Proportion
Using the similarity of triangles, we can set up the following proportion:
- Height of the stick / Length of the stick's shadow = Height of the tower / Length of the tower's shadow
This translates to:
- 12 cm / 8 cm = Height of the tower / 4000 cm
Calculating the Height of the Tower
To find the height of the tower, we can rearrange the proportion:
- Height of the tower = (12 cm / 8 cm) * 4000 cm
Now, simplify the calculation:
- Height of the tower = (12 / 8) * 4000
- Height of the tower = 1.5 * 4000 = 6000 cm
Since 1 meter equals 100 cm, we convert 6000 cm into meters:
- Height of the tower = 6000 cm / 100 = 60 m
Conclusion
The height of the tower is 60 m, which corresponds to option B. This consistent ratio method demonstrates how the lengths of shadows can help determine the height of larger structures based on smaller known measurements.
To find the height of the tower based on the shadow lengths, we can use the concept of similar triangles. The ratio of the height of an object to the length of its shadow remains constant for both the stick and the tower since they are being illuminated by the same light source.
Given Data
- Height of the stick: 12 cm
- Length of the stick's shadow: 8 cm
- Length of the tower's shadow: 40 m (which is 4000 cm for consistent units)
Setting Up the Proportion
Using the similarity of triangles, we can set up the following proportion:
- Height of the stick / Length of the stick's shadow = Height of the tower / Length of the tower's shadow
This translates to:
- 12 cm / 8 cm = Height of the tower / 4000 cm
Calculating the Height of the Tower
To find the height of the tower, we can rearrange the proportion:
- Height of the tower = (12 cm / 8 cm) * 4000 cm
Now, simplify the calculation:
- Height of the tower = (12 / 8) * 4000
- Height of the tower = 1.5 * 4000 = 6000 cm
Since 1 meter equals 100 cm, we convert 6000 cm into meters:
- Height of the tower = 6000 cm / 100 = 60 m
Conclusion
The height of the tower is 60 m, which corresponds to option B. This consistent ratio method demonstrates how the lengths of shadows can help determine the height of larger structures based on smaller known measurements.
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A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time, a tower casts a shadow 40 m long on the ground. The height of the tower isa)72 mb)60 mc)65 md)70 mCorrect answer is option 'B'. Can you explain this answer?
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