Final answer:
To calculate the length of the scale model plane using the scale 52:12, we simplify the scale and set up a proportion with the actual length of 106 inches. The result is that the model plane length is 24 inches.
Step-by-step explanation:
To find the length of Avani's scale model of the world's smallest plane, we must use the given scale of 52:12. This means that for every 52 units on the actual plane, the model will have 12 units. We first need to simplify the scale by dividing both numbers by their greatest common divisor, which in this case is 4. The simplified scale becomes 13:3. Now, using the actual length of the plane, which is 106 inches, we set up a proportion with the simplified scale:
Actual length / Model length = Scale factor of actual / Scale factor of the model
106 inches / x inches = 13 / 3
After cross-multiplying and solving for x, we find that x = 106 inches * (3 / 13), which simplifies to x = (106 * 3) / 13. By calculating this, we find that x = 24.46 inches, which rounds to 24 inches since lengths are generally rounded to the nearest whole number.
Therefore, the length of the scale model of the plane is 24 inches.