Question

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

Answer 1

$\begin{array}{c}In\Delta ABC\&\Delta ADE\\ \angle A=\angle A\&\angle ADE=\angle ABC\\ \therefore \Delta ABC\sim \Delta ADE\left(AAsimilarity\right)\\ \therefore \frac{AB}{AD}=\frac{AC}{AE}\\ \frac{8.5}{4}=\frac{AC}{8}\\ \therefore AC=\frac{8.5\times 8}{4}=17cm.\end{array}$