Question 1

(i) In $\triangle ABC$, $DE \parallel BC$ with $D$ on $AB$ and $E$ on $AC$. If $AB = 12\ \text{cm}$, $AC = 9\ \text{cm}$ and $AD = 4\ \text{cm}$, find $EC$.

(ii) In $\triangle ABC$, $DE \parallel BC$ with $D$ on $AB$ and $E$ on $AC$. If $AB = 8\ \text{cm}$, $BC = 6\ \text{cm}$ and $DE = 3\ \text{cm}$, find $AD\,.$