[tex]x=44[/tex]
1) In this problem, we need to find the constant of proportionality assuming these triangles are similar. So let's divide each corresponding leg:
[tex]\frac{22}{18}=\frac{33}{27}\Rightarrow\:k=\frac{11}{9}[/tex]
2) So, based on that constant of proportionality (k) we can find the missing leg.
[tex]\begin{gathered} x\div\frac{11}{9}=36 \\ \\ x\cdot\frac{9}{11}=36 \\ \\ 11\times\frac{9}{11}x=36\times11 \\ \\ 9x=396 \\ \\ \frac{9x}{9}=\frac{396}{9} \\ \\ x=44 \end{gathered}[/tex]
Note that since the triangle on the top is larger than the one on the bottom, we can tell that x must be larger than 36.
