Question
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
Answers
GPT 3.5
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
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