Question

the table below gives the dimensions of a bridge and a scale model of the bridge. find the scale factor of the model. (the scale factor to get the model from the bridge) write your answer as a fraction in simplest form. scale factor:

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) from the bridge (original) to the model (new) is given by \(k=\frac{\text{model dimension}}{\text{bridge dimension}}\).

Step2: Calculate scale factor using width

Using the width values: \(k_1=\frac{5}{45}=\frac{5\div5}{45\div5}=\frac{1}{9}\)

Step3: Verify using height

Using the height values: \(k_2 = \frac{6}{54}=\frac{6\div6}{54\div6}=\frac{1}{9}\)

Step4: Verify using length

Using the length values: \(k_3=\frac{7}{63}=\frac{7\div7}{63\div7}=\frac{1}{9}\)

Answer:

\(\frac{1}{9}\)