Question

$D$ and $F$ are mid-points of sides $AB$ and $AC$ of a triangle $ABC$. A line through $F$ and parallel to $AB$ meets $BC$ at point $E$.
Find $AB$, if $EF=4.8cm$.

Answer 1

Since $F$ is the midpoint and $EF\parallel AB$.
Therefore $E$ is the midpoint of $BC$
So $BE=\frac{1}{2}BC$ and $BF=\frac{1}{2}AB$ ......(1)
Since $D$ and $F$ are the midpoint of $AB$ and $AC$
Therefore $DE\parallel BC$.
So $DF=\frac{1}{2}BC$ and $DB=\frac{1}{2}AB$ ......(2)
From $\left(1\right),\left(2\right)$ we get
$BD=EF$ ...(3)
So, from (1) and (3)

$AB=2EF$

Since

$AB=2EF$
$=2\times 4.8$
$=9.6cm$