Solution:
The triangles are similar if;
[tex]\frac{|AB|}{|UV|}=\frac{|BC|}{|VT|}=\frac{|AC|}{|UT|}[/tex]
Thus, we have;
[tex]\frac{16}{24}=\frac{14}{21}=\frac{12}{18}[/tex]
Then;
Triangle ABC is similar to triangle UVT.
The scale factor is;
[tex]\frac{2}{3}[/tex]
