Question

In a $\Delta ABC$, $D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $DE||BC$.
If $AD=2.5cm,BD=3.0cm$ and $AE=3.75cm$, find the length of $AC$.

Answer 1

$\begin{array}{c}In\Delta ABC\&\Delta ADE\\ \angle A=\angle A\&\angle ABC=\angle ADE\\ \Delta ABC\sim \Delta ADE\\ \therefore \frac{AB}{AD}=\frac{AC}{AE}\\ \frac{2.5+3}{2.5}=\frac{AC}{3.75}\\ \therefore AC=\frac{5.5\times 3.75}{2.5}\\ =8.25cm\end{array}$