A tree is broken at a height of `5 m` from the ground and its top touches the ground at a distance of `12 m` from the base of the tree. Find the original height of the tree

Options

A. `17m`
B. `18m`
C. `16m`
D. `14m`

Explanation

To find the original height of the tree that was broken, we can use the Pythagorean theorem. Here are the steps to solve the problem:

### Step-by-Step Solution:

1. **Identify the Parts of the Triangle**:
- Let the point where the tree is broken be point A (5 m above the ground).
- Let the point where the top of the tree touches the ground be point B (12 m from the base of the tree).
- Let the base of the tree be point C (where the tree stands upright).

2. **Visualize the Triangle**:
- When the tree breaks, it forms a right triangle with:
- AB = height from the ground to the break point = 5 m
- BC = horizontal distance from the base of the tree to where the top touches the ground = 12 m
- AC = the length of the broken part of the tree (hypotenuse).

3. **Apply the Pythagorean Theorem**:
- According to the Pythagorean theorem, in a right triangle:
\[ AC^2 = AB^2 + BC^2 \]
- Substitute the known values:
\[ AC^2 = 5^2 + 12^2 \]
\[ AC^2 = 25 + 144 \]
\[ AC^2 = 169 \]

4. **Calculate AC**:
- Now, take the square root of both sides to find AC:
\[ AC = \sqrt{169} = 13 \text{ m} \]

5. **Find the Original Height of the Tree**:
- The original height of the tree is the sum of the height at which it broke (AB) and the length of the broken part (AC):
\[ \text{Original Height} = AB + AC = 5 \text{ m} + 13 \text{ m} = 18 \text{ m} \]

### Final Answer:
The original height of the tree is **18 meters**.

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