Suppose, \[\vartriangle ABC\text{ }\sim\text{ }\vartriangle DEF\]
So,
\[AB/DE\text{ }=\text{ }BC/EF\]
\[=\text{ }AC/DF\]
Or,
\[=\text{ }\left( AB+BC+AC \right)/\left( DE+EF+DF \right)\]
\[=\text{ }Perimeter\text{ }of\text{ }\Delta \text{ }ABC/Perimeter\text{ }of\text{ }\Delta \text{ }DEF\]
So,
\[Perimeter\text{ }of\text{ }\Delta \text{ }ABC/Perimeter\text{ }of\text{ }\Delta \text{ }DEF\]
\[=\text{ }AB/DE\]
Hence,
\[30/24\text{ }=\text{ }12/DE\]
\[DE\text{ }=\text{ }9.6\text{ }cm\]