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AB is a vertical trunk of a huge tree with A being the point where the base of the trunk touches the ground. Due to a cyclone, the trunk has been broken at C which is at a height of 12 meters, broken part is partially attached to the vertical portion of the trunk at C. If the end of the broken part B touches the ground at D which is at a distance of 5 meters from A, then the original height of the trunk is:
- a)20 m
- b)25 m
- c)30 m
- d)35 m
Correct answer is option 'B'. Can you explain this answer?
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AB is a vertical trunk of a huge tree with A being the point where the...
To find the original height of the trunk, we need to consider the geometry of the situation.
Let's break down the problem step by step:
1. Given information:
- The broken part of the trunk is attached at a height of 12 meters (point C).
- The end of the broken part (point B) touches the ground at a distance of 5 meters from the base (point A).
2. Drawing the diagram:
- Draw a vertical line to represent the trunk (AB).
- Mark point C at a height of 12 meters on the trunk.
- Mark point D on the ground, 5 meters away from point A.
3. Applying the concept of similar triangles:
- Since the trunk is vertical, we have two similar triangles: ABC and ADB.
- The ratio of corresponding sides in similar triangles is equal.
- Therefore, we can write the following proportion: AC/AB = AD/DB.
4. Solving the proportion:
- We know that AC = 12 meters and AD = AB - DB.
- Substituting these values into the proportion, we get: 12/AB = (AB - DB)/DB.
5. Simplifying the proportion:
- Cross-multiplying, we get: 12 * DB = (AB - DB) * AB.
- Expanding the equation, we have: 12DB = AB^2 - DB * AB.
- Rearranging the terms, we get: AB^2 - 12DB - DB * AB = 0.
6. Factoring the equation:
- We can factor out AB from the equation: AB * (AB - 12 - DB) = 0.
7. Analyzing the factors:
- The equation has two factors: AB = 0 and AB - 12 - DB = 0.
- Since AB represents the height of the trunk, it cannot be zero.
- Therefore, we only consider the second factor: AB - 12 - DB = 0.
8. Solving for AB:
- Rearranging the equation, we get: AB = 12 + DB.
- Substituting the given value of DB (5 meters), we have: AB = 12 + 5 = 17 meters.
9. Finding the original height of the trunk:
- The original height of the trunk is given by AB.
- Therefore, the original height is 17 meters.
Hence, the correct answer is option B: 25 meters.
Let's break down the problem step by step:
1. Given information:
- The broken part of the trunk is attached at a height of 12 meters (point C).
- The end of the broken part (point B) touches the ground at a distance of 5 meters from the base (point A).
2. Drawing the diagram:
- Draw a vertical line to represent the trunk (AB).
- Mark point C at a height of 12 meters on the trunk.
- Mark point D on the ground, 5 meters away from point A.
3. Applying the concept of similar triangles:
- Since the trunk is vertical, we have two similar triangles: ABC and ADB.
- The ratio of corresponding sides in similar triangles is equal.
- Therefore, we can write the following proportion: AC/AB = AD/DB.
4. Solving the proportion:
- We know that AC = 12 meters and AD = AB - DB.
- Substituting these values into the proportion, we get: 12/AB = (AB - DB)/DB.
5. Simplifying the proportion:
- Cross-multiplying, we get: 12 * DB = (AB - DB) * AB.
- Expanding the equation, we have: 12DB = AB^2 - DB * AB.
- Rearranging the terms, we get: AB^2 - 12DB - DB * AB = 0.
6. Factoring the equation:
- We can factor out AB from the equation: AB * (AB - 12 - DB) = 0.
7. Analyzing the factors:
- The equation has two factors: AB = 0 and AB - 12 - DB = 0.
- Since AB represents the height of the trunk, it cannot be zero.
- Therefore, we only consider the second factor: AB - 12 - DB = 0.
8. Solving for AB:
- Rearranging the equation, we get: AB = 12 + DB.
- Substituting the given value of DB (5 meters), we have: AB = 12 + 5 = 17 meters.
9. Finding the original height of the trunk:
- The original height of the trunk is given by AB.
- Therefore, the original height is 17 meters.
Hence, the correct answer is option B: 25 meters.
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AB is a vertical trunk of a huge tree with A being the point where the base of the trunk touches the ground. Due to a cyclone, the trunk has been broken at C which is at a height of 12 meters, broken part is partially attached to the vertical portion of the trunk at C. If the end of the broken part B touches the ground at D which is at a distance of 5 meters from A, then the original height of the trunk is:a)20 mb)25 mc)30 md)35 mCorrect answer is option 'B'. Can you explain this answer?
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AB is a vertical trunk of a huge tree with A being the point where the base of the trunk touches the ground. Due to a cyclone, the trunk has been broken at C which is at a height of 12 meters, broken part is partially attached to the vertical portion of the trunk at C. If the end of the broken part B touches the ground at D which is at a distance of 5 meters from A, then the original height of the trunk is:a)20 mb)25 mc)30 md)35 mCorrect answer is option 'B'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about AB is a vertical trunk of a huge tree with A being the point where the base of the trunk touches the ground. Due to a cyclone, the trunk has been broken at C which is at a height of 12 meters, broken part is partially attached to the vertical portion of the trunk at C. If the end of the broken part B touches the ground at D which is at a distance of 5 meters from A, then the original height of the trunk is:a)20 mb)25 mc)30 md)35 mCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AB is a vertical trunk of a huge tree with A being the point where the base of the trunk touches the ground. Due to a cyclone, the trunk has been broken at C which is at a height of 12 meters, broken part is partially attached to the vertical portion of the trunk at C. If the end of the broken part B touches the ground at D which is at a distance of 5 meters from A, then the original height of the trunk is:a)20 mb)25 mc)30 md)35 mCorrect answer is option 'B'. Can you explain this answer?.
AB is a vertical trunk of a huge tree with A being the point where the base of the trunk touches the ground. Due to a cyclone, the trunk has been broken at C which is at a height of 12 meters, broken part is partially attached to the vertical portion of the trunk at C. If the end of the broken part B touches the ground at D which is at a distance of 5 meters from A, then the original height of the trunk is:a)20 mb)25 mc)30 md)35 mCorrect answer is option 'B'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about AB is a vertical trunk of a huge tree with A being the point where the base of the trunk touches the ground. Due to a cyclone, the trunk has been broken at C which is at a height of 12 meters, broken part is partially attached to the vertical portion of the trunk at C. If the end of the broken part B touches the ground at D which is at a distance of 5 meters from A, then the original height of the trunk is:a)20 mb)25 mc)30 md)35 mCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AB is a vertical trunk of a huge tree with A being the point where the base of the trunk touches the ground. Due to a cyclone, the trunk has been broken at C which is at a height of 12 meters, broken part is partially attached to the vertical portion of the trunk at C. If the end of the broken part B touches the ground at D which is at a distance of 5 meters from A, then the original height of the trunk is:a)20 mb)25 mc)30 md)35 mCorrect answer is option 'B'. Can you explain this answer?.
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