In given figure, $\mathrm{DE}\parallel \mathrm{BC}$. If $\mathrm{AD}=3\mathrm{cm}$, $\mathrm{DB}=4\mathrm{cm}$ and $\mathrm{AE}=6\mathrm{cm}$, then find EC.

It is given that $\mathrm{DE}\parallel \mathrm{BC}, \mathrm{AD}=3\mathrm{cm}, \mathrm{DB}=4\mathrm{cm}$, and $\mathrm{AE}=6\mathrm{cm}$. We need to find EC.

Since $\mathrm{DE}\parallel \mathrm{BC}$, from basic proportionality theorem,

$\frac{\mathrm{AD}}{\mathrm{DB}}=\frac{\mathrm{AE}}{\mathrm{EC}}$

On substituting the values, we get the length of AC as

$\begin{array}{l}\Rightarrow \frac{3}{4}=\frac{6}{\mathrm{EC}}\\ \Rightarrow \mathrm{EC}=8\mathrm{cm}\end{array}$

Hence, the length of EC is 8 cm.