Question
A flagpole 3 meters tall casts a shadow 5 meters long at the same time that a building nearby casts a shadow 62 meters long. How tall is the building?
37.2
80
46
100
37.2
80
46
100
Answers
GPT-4o mini
To find the height of the building, we can use the concept of similar triangles. The height of the flagpole and its shadow are proportional to the height of the building and its shadow.
Let \( h \) be the height of the building. We can set up a proportion based on the flagpole and its shadow and the building and its shadow:
\[
\frac{\text{height of flagpole}}{\text{length of flagpole's shadow}} = \frac{\text{height of building}}{\text{length of building's shadow}}
\]
Substituting in the known values:
\[
\frac{3 \text{ m}}{5 \text{ m}} = \frac{h}{62 \text{ m}}
\]
Now, we can cross multiply to solve for \( h \):
\[
3 \text{ m} \cdot 62 \text{ m} = 5 \text{ m} \cdot h
\]
\[
186 = 5h
\]
Now, divide both sides by 5:
\[
h = \frac{186}{5} = 37.2 \text{ m}
\]
Thus, the height of the building is **37.2 meters**.
Let \( h \) be the height of the building. We can set up a proportion based on the flagpole and its shadow and the building and its shadow:
\[
\frac{\text{height of flagpole}}{\text{length of flagpole's shadow}} = \frac{\text{height of building}}{\text{length of building's shadow}}
\]
Substituting in the known values:
\[
\frac{3 \text{ m}}{5 \text{ m}} = \frac{h}{62 \text{ m}}
\]
Now, we can cross multiply to solve for \( h \):
\[
3 \text{ m} \cdot 62 \text{ m} = 5 \text{ m} \cdot h
\]
\[
186 = 5h
\]
Now, divide both sides by 5:
\[
h = \frac{186}{5} = 37.2 \text{ m}
\]
Thus, the height of the building is **37.2 meters**.