Question

1. a telephone booth that is 8 ft tall casts a shadow that is 4 ft long. find the height of a lawn ornament that casts a 2 ft shadow.
2. find the distance between riverside and milton if they are 12 cm apart on a map with a scale of 4 cm : 21 km.

Explanation:

Step1: Set up proportion for height - shadow problem

Let the height of the lawn ornament be $h$. Since the ratio of height to shadow length is the same for both objects, we have the proportion $\frac{8}{4}=\frac{h}{2}$.

Step2: Solve the proportion for $h$

Cross - multiply: $4h = 8\times2$. Then $4h=16$, and $h=\frac{16}{4}=4$.

Step3: Set up proportion for map - distance problem

Let the actual distance be $d$. The scale is $4$ cm : $21$ km, and the map distance is $12$ cm. So we have the proportion $\frac{4}{21}=\frac{12}{d}$.

Step4: Solve the proportion for $d$

Cross - multiply: $4d=12\times21$. Then $4d = 252$, and $d=\frac{252}{4}=63$ km.

Answer:

The height of the lawn ornament is 4 ft.
The distance between Riverside and Milton is 63 km.