In a model of a ship, the mast is `9 cm` high, while the mast of the actual ship is `12 m` high. If the length of the ship is `28 m`, how long is the model ship?

Options

A. `21 cm`
B. `22 cm`
C. `20 cm`
D. `26 cm`

Explanation

To solve the problem, we will use the concept of direct proportions. The heights of the mast and the lengths of the ships are directly proportional to each other.

### Step-by-Step Solution:

1. **Identify the given values:**
- Height of the mast in the model ship (h_model) = 9 cm
- Height of the mast in the actual ship (h_actual) = 12 m
- Length of the actual ship (L_actual) = 28 m
- Length of the model ship (L_model) = ?

2. **Convert the height of the actual mast to the same unit as the model mast:**
- Since the model mast is in centimeters, we convert the actual mast height from meters to centimeters.
- \( h_{actual} = 12 \, \text{m} = 12 \times 100 \, \text{cm} = 1200 \, \text{cm} \)

3. **Set up the proportion:**
- The ratio of the height of the mast to the length of the ship should be the same for both the model and the actual ship.
- Therefore, we can set up the proportion:
\[ \frac{h_{model}}{L_{model}} = \frac{h_{actual}}{L_{actual}} \]
- Substituting the known values:
\[ \frac{9 \, \text{cm}}{L_{model}} = \frac{1200 \, \text{cm}}{28 \, \text{m}} \]

4. **Cross-multiply to solve for \( L_{model} \):**
- Cross-multiplying gives us:
\[ 9 \times 28 = 1200 \times L_{model} \]
- This simplifies to:
\[ 252 = 1200 \times L_{model} \]

5. **Solve for \( L_{model} \):**
- Divide both sides by 1200:
\[ L_{model} = \frac{252}{1200} \]
- Simplifying this fraction:
\[ L_{model} = \frac{21}{100} \, \text{m} \]
- Converting to centimeters (since 1 m = 100 cm):
\[ L_{model} = \frac{21}{100} \times 100 \, \text{cm} = 21 \, \text{cm} \]

6. **Conclusion:**
- The length of the model ship is **21 cm**.