In the given figure, DE || BC such that AE = (1/4) AC. If AB = 6 cm, find AD.

It is given that $D E \| B C, A E=\frac{1}{4} A C$ and $A B=6 \mathrm{~cm}$.

We have to find AD.

Since $\triangle A D E \sim \triangle A B C$

$\Rightarrow \frac{A D}{A B}=\frac{A E}{A C}$

So 

$\Rightarrow \frac{A D}{6 \mathrm{~cm}}=\frac{1 \mathrm{~cm}}{4 \mathrm{~cm}}$

$\Rightarrow 4 \mathrm{~cm} \times A D=6$

$\Rightarrow A D=\frac{6 \mathrm{~cm}}{4 \mathrm{~cm}}$

$\Rightarrow A D=\frac{3 \mathrm{~cm}}{2 \mathrm{~cm}}$

Hence, $A D=1.5 \mathrm{~cm}$