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

Responses

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

Answer 1

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.