Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. triangles fim and lak below are similar, with ( mangle f = mangle l ) and ( mangle m = mangle k ). diagrams: triangle fim with ( fi = 4 ), ( im = 5 ), ( fm = 6 ); triangle lak with ( lk = 12 ). what is the length of ( overline{la} )? options: ( 10 ), ( 8 ), ( 18 ), ( 2 ).

Explanation:

Step1: Identify corresponding sides

Since $\triangle FIM \sim \triangle LAK$, the corresponding sides are proportional. In $\triangle FIM$, $FM = 6$ and in $\triangle LAK$, $LK = 12$. The side $FI = 4$ in $\triangle FIM$ corresponds to $LA$ in $\triangle LAK$.

Step2: Find the scale factor

The scale factor from $\triangle FIM$ to $\triangle LAK$ is $\frac{LK}{FM}=\frac{12}{6} = 2$.

Step3: Calculate length of $LA$

Multiply the length of the corresponding side in $\triangle FIM$ (which is $FI = 4$) by the scale factor. So, $LA=FI\times\text{scale factor}=4\times2 = 8$.

Answer:

8