Solve the following problem using properties of similar triangles a 40 ft flag pole outside an office building cast a 25-ft shadow what is the height of the office building if the shadow It cast is 200 ft long
Let's denote the height of the office building as $h$.
According to the given information, the flag pole has a height of 40 ft and casts a shadow of 25 ft. Using the properties of similar triangles, we can set up a proportion:
$\frac{h}{40} = \frac{200}{25}$
Cross-multiplying, we get:
$25h = 40 \cdot 200$
Simplifying, we find:
$25h = 8000$
Dividing both sides by 25, we obtain:
$h = \frac{8000}{25}$
$h = 320$
Therefore, the height of the office building is 320 ft.