Question

100 ft
25 ft shadow
5 ft shadow
how tall is the flagpole?
a. 10 feet
b. 20 feet
c. 40 feet
d. 80 feet

Explanation:

Step1: Set up proportion

Since the ratio of the height of an object to its shadow length is the same for both the building and the flag - pole, we can set up the proportion $\frac{h_1}{s_1}=\frac{h_2}{s_2}$, where $h_1$ is the height of the building, $s_1$ is the shadow length of the building, $h_2$ is the height of the flag - pole, and $s_2$ is the shadow length of the flag - pole. Let the height of the building $h_1 = 100$ ft, the shadow length of the building $s_1=25$ ft, and the shadow length of the flag - pole $s_2 = 5$ ft. The proportion becomes $\frac{100}{25}=\frac{h_2}{5}$.

Step2: Solve for $h_2$

Cross - multiply the proportion: $25h_2=100\times5$. Then $25h_2 = 500$. Divide both sides by 25: $h_2=\frac{500}{25}=20$ ft.

Answer:

A. 20 feet