Question

triangles fim and lak below are similar, with ( mangle f=mangle l ) and ( mangle m=mangle k ).
what is the length of ( overline{la} )?
10
2
18
8

Explanation:

Step1: Determine the similarity ratio

Since triangles \(FIM\) and \(LAK\) are similar, and \(FM = 6\), \(LK=12\). The similarity ratio \(r=\frac{LK}{FM}=\frac{12}{6} = 2\).

Step2: Find the length of \(LA\)

In \(\triangle FIM\), \(FI = 4\). Let the length of \(LA\) be \(x\). Because of the similarity of the triangles \(\frac{LA}{FI}=r\). Substitute \(r = 2\) and \(FI = 4\) into the equation \(x=2\times4\).

Answer:

\(8\)