Given the triangles are similar, the pair of corresponding sides are proportional.
Then,
[tex]\frac{AB}{ED}=\frac{BC}{EF}[/tex]
Knowing that:
AB = 30
ED = 5
BC = 42
EF = x
Substituting the values:
[tex]\begin{gathered} \frac{30}{5}=\frac{42}{x} \\ 6=\frac{42}{x} \end{gathered}[/tex]
Multiplying both sides by x and then dividing the sides by 6.
[tex]\begin{gathered} 6*x=\frac{42}{x}*x \\ 6x=42 \\ \frac{6x}{6}=\frac{42}{6} \\ x=7 \end{gathered}[/tex]
Answer: x = 7.
