Plant A is currently 20 centimeters tall, and Plant B is currently 12 centimeters tall. The ratio of the heights of Plant A to Plant B is equal to the ratio of the heights of Plant C to Plant D. If Plant C is 54 centimeters tall, what is the height of Plant D, in centimeters?

Options

A. 32.4
B. `44.0`
C. `62.0`
D. `90.0`

Explanation

To solve the problem step by step, we need to find the height of Plant D given the heights of Plant A, Plant B, and Plant C.

### Step-by-Step Solution:

1. **Identify the given heights**:
- Height of Plant A (A) = 20 cm
- Height of Plant B (B) = 12 cm
- Height of Plant C (C) = 54 cm
- Height of Plant D (D) = ?

2. **Set up the ratio**:
The problem states that the ratio of the heights of Plant A to Plant B is equal to the ratio of the heights of Plant C to Plant D. This can be expressed as:
\[ \frac{A}{B} = \frac{C}{D} \]
Substituting the known values:
\[ \frac{20}{12} = \frac{54}{D} \]

3. **Cross-multiply to eliminate the fraction**:
Cross-multiplying gives us:
\[ 20 \cdot D = 12 \cdot 54 \]

4. **Calculate the right side**:
Now, calculate \(12 \cdot 54\):
\[ 12 \cdot 54 = 648 \]
So, we have:
\[ 20D = 648 \]

5. **Solve for D**:
To find D, divide both sides by 20:
\[ D = \frac{648}{20} \]

6. **Perform the division**:
Now, calculate \(648 \div 20\):
\[ D = 32.4 \]

7. **Conclusion**:
The height of Plant D is 32.4 centimeters.

### Final Answer:
The height of Plant D is **32.4 cm**.