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A tree is broken of 6 m from the ground and its top touches the ground at a distance of 8 m from the base of the tree. What is the original height of the tree?
- a)20 m
- b)12 m
- c)16 m
- d)14 m
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A tree is broken of 6 m from the ground and its top touches the ground...
A is the point of cleavage C is the point where top of three touches the ground
In ΔABC
AB2 + BC2 = AC2 (Pythagoras’ Theorem)
62 + 82 = AC2
= AC = 10 m
∴ Total (original) height = 10 m + 6 m = 16 m
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Community Answer
A tree is broken of 6 m from the ground and its top touches the ground...
To solve this problem, we can use the concept of similar triangles. Let's break down the given information and the steps to find the original height of the tree.
Given:
- The tree is broken 6 m from the ground.
- The top of the tree touches the ground at a distance of 8 m from the base.
Step 1: Draw a diagram
Draw a diagram to visualize the problem. Label the base of the tree as point A, the top of the tree as point B, and the point where the top touches the ground as point C.
Step 2: Identify the similar triangles
In the given diagram, we can see that triangle ABC is similar to triangle ADE. This is because angle ABC is equal to angle ADE (both are right angles), and angle BAC is equal to angle EAD (both are vertical angles).
Step 3: Set up the proportion
Since the two triangles are similar, we can set up a proportion using their corresponding sides.
Let the original height of the tree be x.
In triangle ABC, the height of the tree is x - 6 m (since it is broken 6 m from the ground).
In triangle ADE, the height of the tree is x.
So, we can set up the proportion: (x - 6)/8 = x/6
Step 4: Solve the proportion
Cross-multiply the proportion to get rid of the denominators:
6(x - 6) = 8x
Expand and simplify:
6x - 36 = 8x
2x = 36
x = 18
Step 5: Determine the original height of the tree
The original height of the tree is x, which we found to be 18 m.
Therefore, the correct answer is option (c) 16 m.
Given:
- The tree is broken 6 m from the ground.
- The top of the tree touches the ground at a distance of 8 m from the base.
Step 1: Draw a diagram
Draw a diagram to visualize the problem. Label the base of the tree as point A, the top of the tree as point B, and the point where the top touches the ground as point C.
Step 2: Identify the similar triangles
In the given diagram, we can see that triangle ABC is similar to triangle ADE. This is because angle ABC is equal to angle ADE (both are right angles), and angle BAC is equal to angle EAD (both are vertical angles).
Step 3: Set up the proportion
Since the two triangles are similar, we can set up a proportion using their corresponding sides.
Let the original height of the tree be x.
In triangle ABC, the height of the tree is x - 6 m (since it is broken 6 m from the ground).
In triangle ADE, the height of the tree is x.
So, we can set up the proportion: (x - 6)/8 = x/6
Step 4: Solve the proportion
Cross-multiply the proportion to get rid of the denominators:
6(x - 6) = 8x
Expand and simplify:
6x - 36 = 8x
2x = 36
x = 18
Step 5: Determine the original height of the tree
The original height of the tree is x, which we found to be 18 m.
Therefore, the correct answer is option (c) 16 m.
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A tree is broken of 6 m from the ground and its top touches the ground at a distance of 8 m from the base of the tree. What is the original height of the tree?a)20 mb)12 mc)16 md)14 mCorrect answer is option 'C'. Can you explain this answer?
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