If a 1.5 m-tall girl stands at a distance of 3 m from a lamp-post and casts a shadow of length `4.5 m` on the ground, then the height of the lamp-post is

Options

A. `1.5 m`
B. `2m`
C. `2.5 m`
D. `2.8 m`

Explanation

To find the height of the lamp-post, we can use the concept of similar triangles. Here’s a step-by-step solution:

### Step 1: Understand the scenario
We have a girl who is 1.5 m tall standing 3 m away from a lamp-post. The girl casts a shadow of 4.5 m. We need to find the height of the lamp-post.

### Step 2: Set up the triangles
We can form two right triangles:
1. Triangle formed by the girl and her shadow.
2. Triangle formed by the lamp-post and its shadow.

Let:
- Height of the girl = 1.5 m
- Distance of the girl from the lamp-post = 3 m
- Length of the shadow of the girl = 4.5 m
- Height of the lamp-post = H (unknown)
- Total distance from the lamp-post to the end of the lamp-post's shadow = 4.5 m + 3 m = 7.5 m

### Step 3: Write the proportion using similar triangles
Since the triangles are similar, we can set up the following proportion:
\[ \frac{\text{Height of the girl}}{\text{Length of the girl's shadow}} = \frac{\text{Height of the lamp-post}}{\text{Total length of the lamp-post's shadow}} \]
This can be expressed as:
\[ \frac{1.5}{4.5} = \frac{H}{7.5} \]

### Step 4: Cross-multiply to solve for H
Cross-multiplying gives us:
\[ 1.5 \times 7.5 = H \times 4.5 \]
Calculating the left side:
\[ 11.25 = H \times 4.5 \]

### Step 5: Isolate H
To find H, divide both sides by 4.5:
\[ H = \frac{11.25}{4.5} \]

### Step 6: Calculate H
Now, performing the division:
\[ H = 2.5 \text{ m} \]

### Conclusion
The height of the lamp-post is **2.5 meters**.

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