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=(12)/(8) \\ k=(3)/(2) \end{gathered}`

Therefore:

`\begin{gathered} k\cdot FJ=LA \\ so\colon \\ (3)/(2)\cdot6=LA \\ LA=9 \end{gathered}`