Question

6 lin has a scale model of a modern train. the model is created at a scale of 1 to 43.

a. the height of the model train is 102 millimeters. what is the actual height of the train in meters? explain your reasoning.

Explanation:

Step1: Understand the scale

The scale is 1 to 43, meaning 1 unit of the model corresponds to 43 units of the actual train. So if the model height is \( h_{model} \), the actual height \( h_{actual} = h_{model} \times 43 \).
Given \( h_{model} = 102 \) millimeters. So \( h_{actual} = 102 \times 43 \) millimeters.

Step2: Calculate actual height in millimeters

\( 102\times43 = (100 + 2)\times43 = 100\times43 + 2\times43 = 4300 + 86 = 4386 \) millimeters.

Step3: Convert millimeters to meters

Since 1 meter = 1000 millimeters, to convert millimeters to meters, we divide by 1000. So \( h_{actual (meters)}=\frac{4386}{1000}=4.386 \) meters.

Answer:

The actual height of the train is \( 4.386 \) meters.