Is it true that for every 2 regular languages $L\_1$, $L\_2$ the language $$L=\{uv\ |\ u\ \text{is in}\ L\_1, v\ \text{is in}\ L\_2\ \text{and}\ |v| = 2|u|\}$$ is context free?
I think that it isn't, because if $L\_1$ & $L\_2$ are regular then they are context-free and have grammars but I don't see construction that can limit the length of $u$ and $v$.