Question

In $△ABC$ $DE||BC$ and $\frac{AD}{DB}=\frac{3}{5}$$AC=5.6$ find $AE$ ?

Answer 1

given that $\frac{AD}{DB}$=$\frac{3}{5}$

$AC=5.6$ cm ; therefore $AC-AE=EC$

Since $DE||BC$

$\frac{AB}{DB}=\frac{AE}{EC}$

reversing $\frac{DB}{AD}=\frac{AC}{AE}$

adding 1 then cross multiplying

$\frac{AB+AD}{AD}=\frac{EC+AE}{AE}$

$\frac{AB}{AD}=\frac{AC}{AE}$

$\frac{8}{3}=\frac{5.6}{AE}$

$AE=5.6\times \frac{3}{8}$

$AE=2.1$ cm

$EC=3.5$ cm

Therefore $5.6-2.1=3.5$ cm