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} )? 18 2 8 10

Explanation:

Step1: Find the scale factor

Since the triangles are similar, the ratio of corresponding sides is equal. The ratio of \(MK\) to \(LK\) is \(\frac{12}{8}=\frac{3}{2}\).

Step2: Calculate the length of \(LA\)

The side \(FI = 4\). Let the length of \(LA\) be \(x\). Using the scale factor \(\frac{3}{2}\), we have \(x=4\times\frac{3}{2}\).

$$x = 6\times3= 18$$

Answer:

18