Sides of Similar Figures Quick Check

Question

4 of 54 of 5 Items

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

5 feet
5 feet

400 feet
400 feet

320 feet
320 feet

125 feet

Answer 1

The height of the office building can be determined using the property of similar triangles.

Let's set up a proportion using the corresponding sides of the two triangles:

40 feet (height of flagpole) / 25 feet (shadow of flagpole) = x (height of office building) / 200 feet (shadow of office building)

Cross multiply and solve for x:

40 * 200 = 25 * x

8000 = 25x

Divide both sides by 25:

x = 320

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

Answer: 320 feet