To solve this problem, we can use the property of similar triangles. The ratio of the height of an object to the length of its shadow will be the same for both the flagpole and the office building.
Let's denote the height of the office building as \( h \).
From the problem, we have the following ratios based on the heights and shadow lengths:
\[ \frac{\text{Height of the flagpole}}{\text{Shadow of the flagpole}} = \frac{\text{Height of the office building}}{\text{Shadow of the office building}} \]
Plugging in the values we know:
\[ \frac{40 \text{ feet}}{25 \text{ feet}} = \frac{h}{200 \text{ feet}} \]
Now we can cross-multiply to solve for \( h \):
\[ 40 \times 200 = 25 \times h \]
This simplifies to:
\[ 8000 = 25h \]
Now, divide both sides by 25:
\[ h = \frac{8000}{25} = 320 \text{ feet} \]
Thus, the height of the office building is 320 feet.
The correct response is:
320 feet
1 answer