Sides of Similar Figures Quick Check
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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
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