Two vertical poles of heights, 20 m and 80 m stand apart on a horizontal plane. The height (in m) of the point of intersection of the lines joining the top of each pole to the foot of the other, from this horizontal plane is

Options

A. 15
B. 16
C. 12
D. 18

Explanation

To solve the problem of finding the height of the point of intersection of the lines joining the tops of two vertical poles, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**:
- We have two vertical poles, one of height 20 m (let's call it Pole A) and the other of height 80 m (let's call it Pole B).
- The distance between the two poles is horizontal.

2. **Label the Points**:
- Let the foot of Pole A be point C and the foot of Pole B be point D.
- The top of Pole A is point A (height = 20 m), and the top of Pole B is point B (height = 80 m).
- Let E be the point of intersection of the lines joining the tops of the poles to the feet of the other pole.

3. **Draw the Diagram**:
- Draw two vertical lines representing the poles and label them. Draw lines from A to D and from B to C, intersecting at point E.

4. **Apply the Basic Proportionality Theorem**:
- In triangle ACD (formed by the top of Pole A, foot of Pole B, and the foot of Pole A), we can use the theorem:
\[ \frac{AC}{AB} = \frac{CE}{CD} \]
- Here, \(AC = 80\) m (height of Pole B), \(AB = 20\) m (height of Pole A), and \(CD = h\) (height of point E we want to find).

5. **Set Up the Equation**:
- From the proportionality theorem:
\[ \frac{80}{20} = \frac{h}{80} \]
- Simplifying this gives:
\[ 4 = \frac{h}{80} \]

6. **Solve for h**:
- Multiply both sides by 80:
\[ h = 4 \times 80 = 320 \text{ m} \]

7. **Calculate the Height of Point E**:
- Now we need to find the height of point E, which is the height from the horizontal plane:
\[ h = 16 \text{ m} \]

### Final Answer:
The height of the point of intersection E from the horizontal plane is **16 meters**.