Question

$D$ and $E$ are points on the sides $AB$ and $AC$ respectively of a $\Delta ABC$ such that $DE||BC$. If $AD=3.6cm,AB=10cm$ and $AE=4.5cm$, find $EC$ and $AC$.

Answer 1

From given triangle, points $D$ and $E$ are on the sides $AB$ and $AC$ respectively such that $DE||BC$.

$AD=3.6cm,AB=10cm$ and $AE=4.5cm$.

By Basic Proportonality Theorem:

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

Here $DB=AB-AD=10-3.6=6.4cm$

$\Rightarrow EC=\frac{4.5}{3.6}\times 6.4$

or $EC=8cm$

And, $AC=AE+EC$

$AC=4.5+8=12.5cm$