Answer:
Missing side length = 54
Step-by-step explanation:
If both the triangles given in the picture are similar their corresponding sides will be proportional.
By applying this rule in the given similar triangles,
[tex]\frac{35}{30}=\frac{49}{42}=\frac{63}{6x-6}[/tex]
[tex]\frac{7}{6}=\frac{7}{6}= \frac{63}{6x-6}[/tex]
[tex]\frac{7}{6}= \frac{63}{6x-6}[/tex]
[tex]\frac{1}{6}= \frac{9}{6x-6}[/tex]
[tex]\frac{1}{6}= \frac{9}{6(x-1)}[/tex]
[tex]1=\frac{9}{x-1}[/tex]
[tex]x-1=9[/tex]
[tex]x=10[/tex]
Therefore, missing side length = [tex]6x-6[/tex]
= [tex]6(x-1)[/tex]
= [tex]6(10-1)[/tex]
= [tex]6\times 9[/tex]
= [tex]54[/tex]
