Question

a bridge is 300 meters long and 50 meters wide. you need to create a model that can fit on a display board with a maximum length of 1.5 meters. what is the maximum model width in meters? use the keypad to enter your answer in the box. the maximum model width is meters.

Explanation:

Step1: Find the scale factor

The actual length of the bridge is \(300\) meters and the model length is \(1.5\) meters. The scale factor \(k\) is the ratio of the model length to the actual length. So, \(k=\frac{1.5}{300}=\frac{1}{200}\)

Step2: Calculate the model width

The actual width of the bridge is \(50\) meters. Let the model width be \(x\) meters. Since the scale factor is the same for length and width in a similar - shaped model (assuming the model is a scaled - down version of the bridge), we use the proportion \(\frac{x}{50}=\frac{1.5}{300}\)

Cross - multiply: \(300x = 1.5\times50\)

\(300x=75\)

Solve for \(x\): \(x=\frac{75}{300}=0.25\)

Answer:

\(0.25\)