Question

12/09 - similarity word problems - l
possible points: 1.92
a flagpole 3 meters tall casts a shadow 5 meters long at the same time that a building nearby casts a shadow 72 meters long. how tall is the building?
the building is meters tall.

Explanation:

Step1: Set up proportion

Let \( h \) be the height of the building. Since the triangles formed by the flagpole, its shadow, the building, and its shadow are similar, we have the proportion \(\frac{3}{5}=\frac{h}{72}\).

Step2: Solve for \( h \)

Cross - multiply: \( 5h = 3\times72 \).
Calculate \( 3\times72 = 216 \), so \( 5h=216 \).
Then \( h=\frac{216}{5}=43.2 \).

Answer:

\( 43.2 \)