Question

In ΔABC, D and E are points on AB and AC, respectively, such that AD = 5 cm, DB = 8 cm and DE ∥ BC. If AC = 6.5 cm, find AE.

Answer 1

Let AE be x cm.
Then, EC = (AC - AE) cm = (6.5 - x) cm
In Δ ABC, $\mathrm{DE}\parallel \mathrm{BC}$
∴ $\frac{\mathrm{AD}}{\mathrm{DB}}=\frac{\mathrm{AE}}{\mathrm{EC}}$ [By Thales' theorem]
$\Rightarrow \frac{5}{8}=\frac{x}{\left(6.5-x\right)}$
$\Rightarrow 5\left(6.5-x\right)=8x$
$\Rightarrow 13x=32.5$
$\Rightarrow x=\frac{32.5}{13}=2.5$
Hence, AE = 2.5 cm.