Question

$BD$ is a median of a triangle $ABC$. $F$ is a point on $AB$ such that $CF$ intersects $BDatE$ and $BE=ED$. If $BF=5cm$, $BA$ is equal to

• A. $10$
• B. $12$
• C. $15$
• D. $17$

Answer 1

The correct option is C

$15$

Let $G$ is a point on $EC$ then $FE=EG$,
Join $GandD$and $GandB$, $DandF$.
$\therefore BGDF$ is a parallelogram.
$BF=GD=5cm$
$GD\parallel AFthenAF=2GD=10cm$ (By mid-point theorem)
Now, $BA=BF+AF=5+10=15cm$

Hence, the correct option is C.