Two triangles are similar if their corresponding sides are proportional.

Two triangles are similar if their corresponding angles are equal.

In a $\Delta ABC,D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $DE\parallel BC$.
If $\frac{AD}{DB}=\frac{2}{3}$ and $AC=18 \mathrm{cm}$, if $AE=K \mathrm{cm}$, then find the value of $K.$

In a $\Delta ABC,D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $DE\parallel BC$. If $AD=4 \mathrm{cm}, DB=4.5 \mathrm{cm}$and $AE=8 \mathrm{cm}$ and $AC=K \mathrm{cm}$, find $K$.

In a $\Delta ABC,D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $DE\parallel BC$. If $AD=2 \mathrm{cm}, AB=6 \mathrm{cm}$and $AC=9 \mathrm{cm}$ and $AE=K \mathrm{cm}$, find $K$.