Question

1. two scale models were made of a bridge. why is the 1:300 scale model smaller than the 1:200 scale model? by what percentage is it smaller?

Explanation:

Step1: Understand the scale ratio concept

A scale of \(1:n\) means \(1\) unit on the model represents \(n\) units in real - life. For a \(1:300\) scale model, \(1\) unit on the model represents \(300\) units in real - life. For a \(1:200\) scale model, \(1\) unit on the model represents \(200\) units in real - life. Let the real - life length be \(L\). Then the length of the \(1:300\) model is \(x=\frac{L}{300}\), and the length of the \(1:200\) model is \(y = \frac{L}{200}\).

Step2: Calculate the percentage difference

The formula for percentage difference is \(\text{Percentage}=\frac{y - x}{y}\times100\%\). Substitute \(x=\frac{L}{300}\) and \(y=\frac{L}{200}\) into the formula.

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Answer:

The \(1:300\) scale model is smaller because for the same real - life object, a larger denominator in the scale ratio (\(1:n\)) means a smaller model. It is smaller by approximately \(33.3\%\).