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)
Let the height of the office building be $x$ feet. By similar triangles, we have $\frac{x}{200}=\frac{40}{25}$. Cross-multiplying gives $25x=40\cdot 200$, so $x=\boxed{320}$.
answer?
The height of the office building is 320 feet.
The sides of a triangular path measure 7 m, 9 m, and 11 m. Find the perimeter of a similar triangle in which the shortest side has a length of 21 meters.(1 point) Responses 81 m 81 m 21 m 21 m 33 m 33 m 27 m 27 m
Let the sides of the similar triangle be $21m$, $x$, and $y$. Since the triangles are similar, we have the ratio $\frac{x}{7}=\frac{y}{9}=\frac{21}{11}$. Solving for $x$ and $y$, we get $x=\frac{7}{21}\cdot 21=7$ and $y=\frac{9}{21}\cdot 21=9$.
Therefore, the perimeter of the similar triangle is $21+7+9=\boxed{37 \text{ m}}$.