A tree is 12m tall and casts an 8 m long shadow. At the same time, a flag pole casts a 100m long shadow. How long is the flag pole?

Options

A. 150m
B. 200m
C. 125m
D. 115m

Answer

To solve the problem, we can use the concept of similar triangles, which states that the ratios of the corresponding sides of similar triangles are equal.

### Step-by-Step Solution:

1. **Identify the given information:**
- Height of the tree = 12 m
- Length of the tree's shadow = 8 m
- Length of the flagpole's shadow = 100 m
- Height of the flagpole = ? (This is what we need to find)

2. **Set up the proportion using similar triangles:**
Since the tree and the flagpole are casting shadows at the same time, we can set up the following proportion based on their heights and shadow lengths:
\[ \frac{\text{Height of Tree}}{\text{Length of Tree's Shadow}} = \frac{\text{Height of Flagpole}}{\text{Length of Flagpole's Shadow}} \]
Plugging in the known values:
\[ \frac{12 \text{ m}}{8 \text{ m}} = \frac{h}{100 \text{ m}} \]
where \( h \) is the height of the flagpole.

3. **Cross-multiply to solve for \( h \):**
\[ 12 \text{ m} \times 100 \text{ m} = 8 \text{ m} \times h \]
\[ 1200 = 8h \]

4. **Isolate \( h \):**
\[ h = \frac{1200}{8} \]
\[ h = 150 \text{ m} \]

5. **Conclusion:**
The height of the flagpole is 150 m.

### Final Answer:
The flagpole is 150 meters tall.