The shadow of a 5-m-long stick is 2m long. At the same time, the length of the shadow of a `12.5m` high tree is

Options

A. `3m`
B. `3.5 m`
C. `4.5 m`
D. `5 m`

Explanation

To solve the problem, we will use the concept of similar triangles, which states that the ratios of the lengths of objects to their shadows will be equal when measured at the same time.

### Step-by-Step Solution:

1. **Identify the lengths and shadows:**
- Length of the stick (L1) = 5 m
- Length of the shadow of the stick (S1) = 2 m
- Length of the tree (L2) = 12.5 m
- Length of the shadow of the tree (S2) = ?

2. **Set up the proportion:**
Since the stick and the tree cast shadows at the same time, we can set up the following proportion based on the similarity of triangles:
\[ \frac{L1}{S1} = \frac{L2}{S2} \]

3. **Substitute the known values into the proportion:**
\[ \frac{5}{2} = \frac{12.5}{S2} \]

4. **Cross-multiply to solve for S2:**
\[ 5 \cdot S2 = 12.5 \cdot 2 \]

5. **Calculate the right-hand side:**
\[ 5 \cdot S2 = 25 \]

6. **Divide both sides by 5 to isolate S2:**
\[ S2 = \frac{25}{5} = 5 \text{ m} \]

### Final Answer:
The length of the shadow of the 12.5 m high tree is **5 m**.