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
320 feet
320 feet
400 feet
400 feet
125 feet
Let's use similar triangles to solve this problem.
We have two similar triangles - the triangle formed by the flagpole, its shadow, and the ground, and the triangle formed by the office building, its shadow, and the ground.
Let's denote the height of the office building as "h" and the length of its shadow as "s". Similarly, let's denote the height of the flagpole as 40 feet and the length of its shadow as 25 feet.
We can set up a proportion between the corresponding sides of these triangles:
(h / s) = (40 / 25)
Cross-multiplying, we get:
25h = 40s
Now we can substitute the given values into this equation:
25h = 40 * 200
Simplifying, we get:
25h = 8000
Dividing both sides by 25, we get:
h = 320
Therefore, the height of the office building is 320 feet.
The correct answer is: 320 feet