Question

In triangle $ABC$; $D$ and $E$ are mid-points of the sides $AB$ and $AC$ respectively. Through $E$, a straight line is drawn parallel to $AB$ to meet $BC$ at $F$. Quadrilateral $BDEF$ is a parallelogram.If $AB=16$ cm, $AC=12$ cm and $BC=18$ cm, find the perimeter of the parallelogram $BDEF$.

• A. 36 cm
• B. 44 cm
• C. 34 cm
• D. 54 cm

Answer 1

The correct option is C 34 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
Perimeter of BDEF = $2(BD+BF)$ (Opposite sides of parallelogram are equal)
Perimeter of BDEF = $AB+BC$ (D and F are mid points of AB and BC respectively)
Perimeter of BDEF = $16+18$
Perimeter of BDEF = $34$ cm