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 step by step, we will use the concept of direct proportions.

### Step 1: Understand the Proportions
We know that the dimensions of the model ship and the actual ship are directly proportional. This means that the ratio of the corresponding dimensions of the model and the actual ship will be the same.

### Step 2: Write Down the Given Information
- Height of the mast in the model ship (x1) = 9 cm
- Height of the mast in the actual ship (y1) = 12 m = 1200 cm (since we need to convert meters to centimeters for consistency)
- Length of the actual ship (y2) = 28 m = 2800 cm
- Length of the model ship (x2) = ? (this is what we need to find)

### Step 3: Set Up the Proportion
Using the direct proportion relationship, we can set up the equation:
\[ \frac{x1}{y1} = \frac{x2}{y2} \]
Substituting the known values:
\[ \frac{9}{1200} = \frac{x2}{2800} \]

### Step 4: Cross-Multiply
To solve for \(x2\), we can cross-multiply:
\[ 9 \times 2800 = 1200 \times x2 \]
This simplifies to:
\[ 25200 = 1200 \times x2 \]

### Step 5: Solve for \(x2\)
Now, divide both sides by 1200 to isolate \(x2\):
\[ x2 = \frac{25200}{1200} \]
Calculating this gives:
\[ x2 = 21 \]

### Step 6: State the Final Answer
The length of the model ship is:
\[ \text{Length of the model ship} = 21 \text{ cm} \]