[tex]28\:\text{cm}[/tex]
Step-by-step explanation:
If the two triangles are similar, then the ratios of their legs are equal.
[tex]\dfrac{x+4}{3x-2} = \dfrac{4.5\:\text{cm}}{9\:\text{cm}}=\dfrac{1}{2}[/tex]
After cross-multiplying, we get
[tex]2x + 8 = 3x - 2 \Rightarrow x = 10[/tex]
Therefore, the length of the leg BC is
[tex]\overline{BC} = 3x - 2 = 3(10) - 2 = 28\:\text{cm}[/tex]
