Question

triangles fim and lak below are similar, and la = ak. what is the length of (overline{la})? options: 9, 4, 10, 16 (triangles: fim has fi=6, im=6, fm=8; lak has lk=12, la=ak)

Explanation:

Step1: Identify similar triangles' sides

Triangle FIM has sides \( FI = 6 \), \( IM = 6 \), \( FM = 8 \). Triangle LAK is isosceles with \( LA = AK \), and \( LK = 12 \). Since they are similar, the ratio of corresponding sides is equal. The ratio of \( LK \) to \( FM \) is \( \frac{12}{8}=\frac{3}{2} \).

Step2: Find length of \( LA \)

In triangle FIM, the equal sides are 6, and in triangle LAK, \( LA = AK \). The corresponding equal sides in FIM (length 6) will scale by \( \frac{3}{2} \). So \( LA = 6\times\frac{3}{2}=9 \).

Answer:

9