On level ground, a vertical rod 12 feet tall casis a shadow 4 feet long, and at the same time a nearby vertical flagpole casts a shadow 12 feet long. How many feet tall is the flagpole?

Options

A. 4
B. 8
C. 12
D. 36

Answer

To solve the problem, we will use the concept of similar triangles. The height of the vertical rod and the height of the flagpole, along with their respective shadows, form two similar triangles.

### Step-by-Step Solution:

1. **Identify the given information:**
- Height of the rod (h1) = 12 feet
- Length of the shadow of the rod (s1) = 4 feet
- Length of the shadow of the flagpole (s2) = 12 feet
- Height of the flagpole (h2) = ?

2. **Set up the proportion using similar triangles:**
Since the triangles formed by the rod and its shadow and the flagpole and its shadow are similar, we can set up the following proportion:
\[ \frac{h1}{s1} = \frac{h2}{s2} \]
Substituting the known values:
\[ \frac{12}{4} = \frac{h2}{12} \]

3. **Cross-multiply to solve for h2:**
Cross-multiplying gives:
\[ 12 \cdot 12 = 4 \cdot h2 \]
This simplifies to:
\[ 144 = 4h2 \]

4. **Isolate h2:**
Divide both sides by 4 to find h2:
\[ h2 = \frac{144}{4} = 36 \text{ feet} \]

5. **Conclusion:**
The height of the flagpole is 36 feet.