A model of a aeroplane (somewhat triangular in shape) is made on the scale of `1 : 100`. The model is 150 cm long, what is the length of the actual aeroplane?

Options

A. 170 m
B. 150 m
C. 200 m
D. 15 m

Answer

To find the length of the actual airplane based on the model's length and the scale, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Scale**: The scale given is 1:100. This means that 1 unit of measurement on the model corresponds to 100 units of measurement on the actual airplane.

2. **Identify the Length of the Model**: The length of the model is given as 150 cm.

3. **Set Up the Proportion**: According to the scale, if the model length is 1 cm, the actual airplane length would be 100 cm. Therefore, we can set up the following proportion:
\[ \text{Model Length} : \text{Actual Length} = 1 : 100 \]
or mathematically,
\[ \frac{\text{Model Length}}{\text{Actual Length}} = \frac{1}{100} \]

4. **Substitute the Model Length**: We know the model length is 150 cm. Let \( x \) be the actual length of the airplane. We can write:
\[ \frac{150}{x} = \frac{1}{100} \]

5. **Cross Multiply to Solve for \( x \)**:
\[ 150 \times 100 = 1 \times x \]
\[ 15000 = x \]

6. **Conclusion**: The length of the actual airplane is \( x = 15000 \) cm.

### Final Answer:
The length of the actual airplane is **15000 cm** or **150 meters**.