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.)
width (feet) model bridge
height (feet) 4 10
length (feet) 6 15
12 30
scale factor:

Explanation:

Step1: Recall scale - factor formula

The scale factor from the actual bridge to the model is the ratio of the dimension of the model to the corresponding dimension of the bridge. We can use any of the three given dimensions (width, height, or length).

Step2: Calculate scale - factor using height

Let's use the height values. The height of the model is 4 feet and the height of the bridge is 10 feet. The scale factor $k$ is given by $k=\frac{\text{Model height}}{\text{Bridge height}}=\frac{4}{10}$.

Step3: Simplify the fraction

Simplify $\frac{4}{10}$ by dividing both the numerator and the denominator by their greatest - common divisor, which is 2. So, $\frac{4\div2}{10\div2}=\frac{2}{5}$.

Answer:

$\frac{2}{5}$