# Dru is challenged by her geometry teacher to estimate the height of the school flag pole without measuring. She decided to walk off the length of the shadow cast by the pole by successively walking...

Dru is challenged by her geometry teacher to estimate the height of the school flag pole without measuring. She decided to walk off the length of the shadow cast by the pole by successively walking the noted length of her own shadow. If Dru is 5 ft 6 in. tall and she estimates the flagpole shadow is 14 times as long as her own shadow, then what is the approximate height of the flag pole?

samhouston | Certified Educator

This problem can be answered using rules of similarity.  The ratios of corresponding sides of similar figures are equal.  In other words, the ratio of the flag pole's height to Dru's height is equal to the ratio of the flag pole's shadow to Dru's shadow.

Dru estimated that the flag pole's shadow is 14 times the length of her shadow.  Therefore, the flag pole's height will be 14 times Dru's height.  Dru is 5 feet 6 inches tall (or 5.5 feet).  Multiply this by 14 to estimate the height of the flag pole.

5.5 * 14 = 77

The approximate height of the flag pole is 77 feet.