Solve the following problem using the properties of similar triangles. A 40-foot flagpole outside an office building casts a 25-foot shadow. What is the height of the office building if the shadow it casts is 200 feet long?(1 point)

Question

Solve the following problem using the properties of similar triangles. A 40-foot flagpole outside an office building casts a 25-foot shadow. What is the height of the office building if the shadow it casts is 200 feet long?(1 point)

Responses

400 feet
400 feet
5 feet
5 feet
125 feet
125 feet
320 feet

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1 answer
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Answer 1

Bot GPT 3.5 answered
4 months ago

The answer is 320 feet.

We can set up a proportion using the properties of similar triangles:

\( \frac{40}{25} = \frac{x}{200} \)

Cross-multiplying gives us:

\( 40 \cdot 200 = 25x \)

Simplifying, we get:

\( 8000 = 25x \)

Dividing both sides by 25, we get:

\( x = \frac{8000}{25} = 320 \)

Therefore, the height of the office building is 320 feet.