Gordon recently learned that his shadow is proportional to his height. He also learned that the shadows of other objects are proportional to their height. At three o'clock, his shadow measured 4 feet and the shadow of the tree in his front yard measured 18 feet. If Gordon is 6 feet tall, how tall is the tree ?

Options

A. 108 feet
B. 72 feet
C. 27 feet
D. 24 feet

Answer

To solve the problem step by step, we will use the concept of proportionality between the height of an object and the length of its shadow.

### Step-by-Step Solution:

1. **Understanding Proportionality**:
We know that the height of an object (h) is proportional to the length of its shadow (s). This can be expressed mathematically as:
\[ h = k \cdot s \]
where \( k \) is a constant of proportionality.

2. **Finding the Constant of Proportionality**:
For Gordon, we are given:
- Height \( h_G = 6 \) feet
- Shadow \( s_G = 4 \) feet

Plugging these values into the proportionality equation:
\[ 6 = k \cdot 4 \]
To find \( k \), we rearrange the equation:
\[ k = \frac{6}{4} = \frac{3}{2} \]

3. **Setting Up the Equation for the Tree**:
Now, we will use the same constant \( k \) to find the height of the tree. We know:
- Shadow of the tree \( s_T = 18 \) feet

We can express the height of the tree \( h_T \) using the same proportionality constant:
\[ h_T = k \cdot s_T \]
Substituting the value of \( k \) and \( s_T \):
\[ h_T = \frac{3}{2} \cdot 18 \]

4. **Calculating the Height of the Tree**:
Now we compute:
\[ h_T = \frac{3 \cdot 18}{2} = \frac{54}{2} = 27 \text{ feet} \]

5. **Conclusion**:
Therefore, the height of the tree is 27 feet.

### Final Answer:
The height of the tree is **27 feet**.