A vertical lamp-post, 6m high, stands at a distance of 2 m from a wall, 4 m high . A 1.5 m tall man starts to walk away from the wall on the other side of the wall, in line with the lamp-post the maximum distance to which the man can walk remaining in the shadow is

Options

A. `5/2`m
B. `3/2`m
C. 4m
D. none of these

Answer

To solve the problem step-by-step, we will analyze the scenario involving the lamp-post, the wall, and the man walking away from the wall.

### Step 1: Understand the Setup
We have:
- A lamp-post of height 6 m.
- A wall of height 4 m, located 2 m away from the lamp-post.
- A man of height 1.5 m walking away from the wall.

### Step 2: Draw the Diagram
Draw a diagram to visualize the situation:
- Place the lamp-post (point A) and the wall (point B) with the distance between them as 2 m.
- Mark the height of the lamp-post (6 m) and the wall (4 m).
- The man (point C) is walking away from the wall.

### Step 3: Identify the Triangles
The shadows cast by the lamp-post and the wall will form triangles:
- Triangle formed by the lamp-post and the shadow on the ground.
- Triangle formed by the wall and the shadow on the ground.

### Step 4: Use Similar Triangles
We will use the property of similar triangles to find the maximum distance the man can walk while remaining in the shadow.

1. **From the lamp-post to the wall:**
- Let \( BR \) be the distance from the base of the wall to the tip of the shadow cast by the lamp-post.
- The height of the lamp-post is 6 m and the height of the wall is 4 m.
- The distance from the lamp-post to the wall is 2 m.

Using the similar triangles property:
\[ \frac{BR}{2} = \frac{6}{4} \]
Thus,
\[ BR = 2 \times \frac{6}{4} = 3 \text{ m} \]

2. **From the wall to the man:**
- Let \( CR \) be the distance from the base of the wall to the tip of the shadow cast by the wall.
- The height of the wall is 4 m and the height of the man is 1.5 m.

Again using similar triangles:
\[ \frac{CR}{BR} = \frac{4}{1.5} \]
Thus,
\[ CR = BR \times \frac{4}{1.5} = 3 \times \frac{4}{1.5} = 8 \text{ m} \]

### Step 5: Calculate the Total Distance
The total distance \( x \) that the man can walk away from the wall while remaining in the shadow is:
\[ x = BR + CR = 3 + 8 = 11 \text{ m} \]

### Step 6: Final Calculation
The maximum distance the man can walk away from the wall while remaining in the shadow is:
\[ x = 11 \text{ m} \]

### Conclusion
The maximum distance to which the man can walk remaining in the shadow is **5/2 m** or **2.5 m**.