Question

El Generico public high school got a new flagpole. But they completely forgot to buy a cord and NO ONE knows how tall the flagpole is! To find out, they decided to use similar figures! As the sun was setting, Bob the janitor set up a 5-foot stick next to the flagpole and compared shadows. The 5-foot stick cast an 8-foot shadow. The shadow of the flagpole was 32-feet long.
Use rules of similar polygons to figure out how tall the flagpole is!

Answer 1

According to the rule of similar polygons the ratio of corresponding sides of two polygons will be the same. So in this case the ratio of original length and shadow of a stick and ratio of length of flagpole and its shadow will be the same.

Length of Stick = 5 feet
Shadow of Stick = 8 feet
Shadow of flagpole = 32 feet
Length of flagpole = x = ? 

Using rule of similar polygon we can write,

$\frac{5}{8}= \frac{x}{32} \\ \\ \frac{5}{8}*32=x \\ \\ x=20$

Therefore, the length of flagpole will be 20 feet.