Answer:
[tex]WS=8\ units[/tex]
Step-by-step explanation:
we know that
If two triangles are similar
then
the ratio of their corresponding sides are equal and the corresponding angles are also equal
In this problem
[tex]\frac{TU}{TR}=\frac{UW}{RS}=\frac{TW}{TS}[/tex]
we have
[tex]TU=3\ units, RS=15\ units, TW=4\ units,TR=9\ units[/tex]
Find the value of TS
[tex]\frac{TU}{TR}=\frac{TW}{TS}[/tex]
substitute
[tex]\frac{3}{9}=\frac{4}{TS}[/tex]
[tex]TS=36/3=12\ units[/tex]
[tex]WS=TS-TW[/tex]
[tex]WS=12-4=8\ units[/tex]
see the attached figure to better understand the problem
