Question

a model of a bridge is 8 centimeters long, while the actual bridge is 32 meters long. what is the scale factor, and how high is the actual bridge if the models height is 5 centimeters? for each box, use the drop - down arrow to choose the correct value. the model has a scale factor of. the actual bridge is meters high.

Explanation:

Step1: Convert units

Since \(1\) meter \( = 100\) centimeters, the actual bridge length \(32\) meters \(=32\times100 = 3200\) centimeters.
The scale factor \(k=\frac{\text{model length}}{\text{actual length}}\). Given model length \(l_m = 8\) cm and actual length \(l_a=3200\) cm, \(k=\frac{8}{3200}=\frac{1}{400}\).

Step2: Find actual height

Let the model height \(h_m = 5\) cm. Using the scale factor relationship \(\frac{h_m}{h_a}=k\), where \(h_a\) is the actual height.
We know \(k=\frac{1}{400}\), so \(h_a=h_m\times400\). Substituting \(h_m = 5\) cm, \(h_a=5\times400 = 2000\) cm.
Converting back to meters: \(h_a=\frac{2000}{100}=20\) meters.

Answer:

The model has a scale factor of \(\frac{1}{400}\). The actual bridge is \(20\) meters high.