Using Similar Triangles to Find Sides

Fint the measure of x given that \triangle ABC is similar to \triangle ADE.

Rendered by QuickLaTeX.com

    \begin{equation*} \frac{\overline{AD}}{\overline{DE}} = \frac{\overline{AB}}{\overline{BC}} \end{equation*}

    \begin{equation*} \frac{4+2}{x} = \frac{4}{2} \end{equation*}

    \begin{equation*} 6(2) = 4x \end{equation*}

    \begin{equation*} \left( \frac{1}{4} \right) \cdot 12 = 4x \cdot \left( \frac{1}{4} \right) \end{equation*}

    \begin{equation*} \boxed{x=3} \end{equation*}