Question

Triangles FIM and LAK below are similar, with mZF = m_L and m2M = m2K.12What is the length of LA?

Answer 1

Since the triangles are similiar, Let:

$k\cdot FM=LK$

where:

k = Constant of proportionality:

$\begin{gathered} 8\cdot k=12 \\ solve_{\text{ }}for_{\text{ }}k\colon \\ k=\frac{12}{8} \\ k=\frac{3}{2} \end{gathered}$

Therefore:

$\begin{gathered} k\cdot FJ=LA \\ so\colon \\ \frac{3}{2}\cdot6=LA \\ LA=9 \end{gathered}$