Question

a model airplane is 12 centimeters long, and the actual airplane is 48 meters long. what is the scale factor, and what is the wingspan of the model if the actual airplanes wingspan is 60 meters? for each box, use the drop - down arrow to choose the correct value. the model has a scale factor of. the wingspan of the model is centimeters.

Explanation:

Step1: Convert actual length to centimeters

Since \(1\) meter \( = 100\) centimeters, the actual airplane length \(48\) meters \(=48\times100 = 4800\) centimeters.
The scale factor \(k=\frac{\text{model length}}{\text{actual length}}\). Given model length \(l_m = 12\) centimeters and actual length \(l_a=4800\) centimeters.

$$k=\frac{12}{4800}=\frac{1}{400}$$

Step2: Find the model wing - span

The actual wing - span \(L_a = 60\) meters \(=60\times100=6000\) centimeters.
Let the model wing - span be \(L_m\). Using the scale factor formula \(k=\frac{L_m}{L_a}\), we can solve for \(L_m\).
Since \(k = \frac{1}{400}\) and \(L_a = 6000\) centimeters, then \(L_m=k\times L_a\)

$$L_m=\frac{1}{400}\times6000 = 15$$

Answer:

The model has a scale factor of \(\frac{1}{400}\). The wingspan of the model is \(15\) centimeters.