8
Explanation
as the triangles are similar we can set a proportion
Step 1
Let
[tex]\text{ratio}=\frac{\text{longest side}}{\text{smallest side}}[/tex]
so
a) for triangle FIM
[tex]\begin{gathered} \text{ratio}=\frac{\text{longest side}}{\text{middle side}} \\ ratio_1=\frac{FM}{FI}=\frac{6}{4}=\frac{3}{2} \\ ratio_1=\frac{3}{2} \end{gathered}[/tex]
b) for triangle LAK
[tex]\begin{gathered} \text{ratio}=\frac{\text{longest side}}{\text{smallest side}} \\ ratio_2=\frac{LK}{LA}=\frac{12}{LA} \\ ratio_2=\frac{12}{LA} \end{gathered}[/tex]
as the tringles are similar, the ratios are similar
hence
[tex]\begin{gathered} \text{ratio}_1=ratio_2 \\ \frac{3}{2}=\frac{12}{LA} \end{gathered}[/tex]
Step 2
now, solve for LA
[tex]\begin{gathered} \frac{3}{2}=\frac{12}{LA} \\ \text{cross multiply } \\ 3\cdot LA=12\cdot2 \\ 3LA=24 \\ \text{divide both sides by 3} \\ \frac{3LA}{3}=\frac{24}{3} \\ LA=8 \end{gathered}[/tex]
therefore, the answer i
8
I hope this helps you
