We can see that sides HG and LK have a ratio of 8:31 between them. Since sides HE and LI are corresponding, then they must have the same ratio. So, we can formulate the following equation:
[tex]\begin{gathered} \frac{HG}{LK}=\frac{HE}{LI} \\ \frac{8}{31}=\frac{11}{LI}\text{ (Replacing)} \\ \frac{8}{31}\cdot LI=11\text{ (Multiplying by LI on both sides of the equation)} \\ 8\cdot LI=11\cdot31\text{ (Multiplying by 31 on both sides of the equation)} \\ LI=\frac{341}{8}\text{ (Dividing by 8 on both sides of the equation)} \\ LI=42.625\text{ (Dividing)} \\ \text{The answer is 42.6 (Rounding to the nearest tenth)} \end{gathered}[/tex]