Question

1. a telephone booth that is 8 ft tall casts a shadow that is 4 ft. long. determine the scale factor and find the height of a lawn ornament that casts a 2 ft shadow.

Explanation:

Step1: Find the scale factor

The scale factor is the ratio of the height of the object to the length of its shadow. For the telephone booth, height is 8 ft and shadow length is 4 ft. So scale factor $k = \frac{\text{height of booth}}{\text{length of booth's shadow}} = \frac{8}{4} = 2$.

Step2: Find the height of the lawn ornament

Let the height of the lawn ornament be $h$. The scale factor is the same, so $k=\frac{h}{\text{length of ornament's shadow}}$. We know $k = 2$ and shadow length is 2 ft. So $2=\frac{h}{2}$, multiplying both sides by 2 gives $h = 2\times2 = 4$ ft.

Answer:

The scale factor is 2 and the height of the lawn ornament is 4 ft.