Question

similar triangles rst and uvw are shown in this diagram. based on the dimensions in the diagram, what is the length, in centimeters, of vw? enter your answer in the answer boxes at the top of the answer grid and completely fill the matching

Explanation:

Step1: Find the scale - factor

Since the two triangles $\triangle RST$ and $\triangle UVW$ are similar, the ratio of corresponding sides is the same. Let the scale - factor be $k$. The ratio of the corresponding sides $UW$ and $RT$ is $k=\frac{UW}{RT}=\frac{9.75}{6.5} = 1.5$.

Step2: Calculate the length of $VW$

Side $VW$ corresponds to side $ST$. We know that $ST = 5$ cm. Using the scale - factor, we can find $VW$ as $VW=k\times ST$. Substituting $k = 1.5$ and $ST = 5$ cm, we get $VW=1.5\times5=7.5$ cm.

Answer:

$7.5$