Question

In triangle $ABC$, $D$ and $E$ are mid-points of sides $AB$ and $BC$ respectively. Also, $F$ is a point in side $AC$ so that $DF$ is parallel to $BC$.

Find the perimeter of parallelogram $DBEF$, if $AB=10$ cm, $BC=8\cdot 4$ cm and $AC=12$ cm,

• A. $28.7$ cm
• B. $22.5$ cm
• C. $18.4$ cm
• D. $18.5$ cm

Answer 1

The correct option is C $18.4$ cm

Given: D and E are mid points of AB and BC respectively. $DF\parallel BC$
Since, $DF\parallel BC$ D is mid point of AB
By converse of mid point theorem, F is mid point of AC and $DF=\frac{1}{2}BC$ (I)
Now, E and F are mid points of BC and AC respectively.Thus, by mid point theorem,
$EF\parallel AB$ or $EF\parallel DB$
Since, opposite sides are parallel to each other. Hence, $DBEF$ is a parallelogram
Perimeter of parallelogram = $2(BE+BD)$ (Opposite sides of parallelogram are equal)
Perimeter of parallelogram = $2(BE+\frac{1}{2}AB)$ (E and D are mid point of BC and AB)
Perimeter of parallelogram = $BC+AB$
Perimeter of parallelogram = $8.4+10$
Perimeter of parallelogram = $18.4$ cm