삼각형의 닮음을 이용한 길이 구하기

문제

다음 그림에서 $\overline{DE} \parallel \overline{BC}$ 이고, $\overline{AD} = 4\text{cm}$, $\overline{DB} = 6\text{cm}$, $\overline{DE} = 6\text{cm}$ 일 때, $\overline{BC}$ 의 길이는?

\begin{tikzpicture}
\coordinate (A) at (0,3);
\coordinate (B) at (-2,0);
\coordinate (C) at (3,0);
\coordinate (D) at ($(A)!0.4!(B)$); % 4/(4+6) = 0.4
\coordinate (E) at ($(A)!0.4!(C)$); % 4/(4+6) = 0.4

\draw (A) node[above] {$A$} -- (B) node[left] {$B$} -- (C) node[right] {$C$} -- cycle;
\draw (D) node[above left] {$D$} -- (E) node[above right] {$E$};

\draw[decorate,decoration={brace,amplitude=5pt},xshift=-4pt,yshift=0pt] (A) -- (D) node[midway,left=5pt] {$4$};
\draw[decorate,decoration={brace,amplitude=5pt},xshift=-4pt,yshift=0pt] (D) -- (B) node[midway,left=5pt] {$6$};

\node at ($(D)!0.5!(E)$) [below] {$6$};
\end{tikzpicture}