Question

In the given figure, $AE\parallel DB,BC=7cm,BD=5cm,DC=4cm$. If $CE=12cm,$ find $AE$ and $AC$.

Answer 1

Consider two triangles $ACE$ and $CDB$

$AE\parallel DB$ ..... [Given in the figure]

By basic proportionality theorem,

$\frac{CD}{CE}=\frac{4}{12}=\frac{1}{3}$

Similarly, $\frac{BC}{AC}=\frac{DB}{AE}=\frac{CD}{CE}=\frac{1}{3}$

$\Rightarrow \frac{7}{AC}=\frac{1}{3}\Rightarrow AC=21cm$

$\frac{5}{AE}=\frac{1}{3}$

$\therefore AE=15cm$