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 is 200 feet long
Let the height of the office building be $h$ feet.
According to the given information, the flagpole is 40 feet tall and casts a shadow that is 25 feet long, and the office building casts a shadow that is 200 feet long.
We can form a proportion using the heights and shadows of the flagpole and office building:
$\frac{40}{25} = \frac{h}{200}$
Solving for $h$:
$40 \times 200 = 25h$
$8000 = 25h$
$h = \frac{8000}{25}$
$h = 320$
Therefore, the height of the office building is 320 feet.