A model of an aeroplane is made to a scale of 1 : 400. Calculate :
the length, in m, of the aeroplane, if length of its model is 16 cm. 

Answer

To solve the problem step by step, we will follow the given information and apply the scale to find the length of the actual aeroplane.

### Step 1: Understand the Scale
The scale of the model is given as 1 : 400. This means that 1 unit of measurement on the model corresponds to 400 units of measurement on the actual aeroplane.

### Step 2: Convert the Length of the Model
The length of the model is given as 16 cm. To work with consistent units, we will convert this length into meters.
- 1 meter = 100 centimeters
- Therefore, 16 cm = 16/100 meters = 0.16 meters.

### Step 3: Apply the Scale to Find the Actual Length
According to the scale, if the model length is 1 meter, then the actual length is 400 meters. Since we have the model length in meters (0.16 m), we can find the actual length of the aeroplane using the scale:
- Actual length = Model length × Scale factor
- Actual length = 0.16 m × 400

### Step 4: Perform the Calculation
Now we will calculate the actual length:
- Actual length = 0.16 × 400
- To make the multiplication easier, we can express 0.16 as a fraction:
- 0.16 = 16/100
- Therefore, Actual length = (16/100) × 400 = (16 × 400) / 100

### Step 5: Simplify the Calculation
Now we can simplify:
- Actual length = (16 × 400) / 100
- Actual length = 6400 / 100
- Actual length = 64 meters.

### Conclusion
The length of the aeroplane is 64 meters.

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