when two triangles are similar it means that both of them share a relation between their sides, and it must be fulfilled on all of its sides.
In order to find x, we need to find first the relationship with a pair of sides that is complete.
We can use sides AB and (AB)'
Then,
[tex]\begin{gathered} AB=k\cdot(AB)^{\prime} \\ 6=k\cdot24 \\ k=\frac{6}{24} \\ k=\frac{1}{4} \end{gathered}[/tex]then use this proportion to find x
[tex]\begin{gathered} AC=k\cdot(AC)^{\prime} \\ 10=\frac{1}{4}\cdot x \end{gathered}[/tex]solve the resulting equation for x
[tex]\begin{gathered} 10\cdot4=x \\ x=40 \end{gathered}[/tex]the missing side is equal to 40.
