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 $EF=4.8$ cm

• A. $5.4\text{cm}$
• B. $1.8\text{cm}$
• C. $3.6\text{cm}$
• D. $9.6\text{cm}$

Answer 1

The correct option is D $9.6\text{cm}$

Given: D and F are mid points of $AB$ and AC respectively.

Hence, by mid point theorem, $DF\parallel BC$
Also, given $BD\parallel EF$

Since, opposite sides are parallel to each other. Hence, $BDEF$ is a parallelogram

$BD=EF$

$\frac{1}{2}AB=EF$ (D is mid point of AB)

$AB=2EF$

$AB=2\left(4.8\right)$

$AB=9.6$ cm