Answer:
20 units
Step-by-step explanation:
To find the measure of side \( WU \) in triangle \( UVW \), we need to use the concept of similarity between triangles.
When two triangles are similar, their corresponding sides are in proportion.
Given that triangle \( RST \) is similar to triangle \( UVW \), we can set up the following proportion using the corresponding sides:
\[
\frac{{\text{Side of UVW}}}{{\text{Side of RST}}} = \frac{{\text{Side of UVW}}}{{\text{Side of RST}}}
\]
So, we have:
\[
\frac{{UV}}{{RS}} = \frac{{UW}}{{RT}}
\]
We're asked to find the measure of side \( UW \).
Now, let's solve for \( UW \) using the given measures:
\[
\frac{{UV}}{{RS}} = \frac{{12}}{{6}} = 2
\]
\[
UW = RT \times 2 = 10 \times 2 = 20
\]
Therefore, the measure of side \( WU \) in triangle \( UVW \) is 20 units.
