Question

In the adjoining figure, DE || BC.
(i) If AD=3.4 cm, AB=8.5 cm and AC=13.5 cm, find AE.
(ii) If $\frac{AD}{DB}=\frac{3}{5}$ and AC=9.6 cm, find AE.

Answer 1

Since DE||BC, we have $\frac{AD}{AB}=\frac{AE}{AC}$
$\frac{3.4}{8.5}-\frac{AE}{13.5}=\frac{3.4\times 13.5}{8.5}=5.4$
Hence, AE=5.4 cm.
(ii) Since DE||BC, we have $\frac{AD}{DB}=\frac{AE}{EC}$
$\frac{AE}{EC}=\frac{3}{5}[\because \frac{AD}{DB}=\frac{3}{5}(Given\left)\right]$
Let AE=x cm. Then, EC=(AC-AE)=(9.6-x)cm.
$\frac{x}{9.6-x}-\frac{3}{5}\Rightarrow 5x=3(9.6-x)$
$\Rightarrow 5x=28.8-3x\Rightarrow 8x=28.8\Rightarrow =\mathrm{3.6.}$
$\Rightarrow AE=3.6cm.$