Question

In the figure, ABCD is a parallelogram. If DE $=$ 4 cm, then BF equals :

• A. 2 cm
• B. 4 cm
• C. 8 cm
• D. 16 cm

Answer 1

The correct option is C 8 cm

$\Rightarrow$ In given figure ABCD is a parallelogram.

$\Rightarrow$ $AB=DC=6cm$ and $AD=BC=3cm$ ---(1) [Opposite sides of parallelogram are parallel and equal]

$\Rightarrow$ We can see in figure DE $\perp$ AB

$\Rightarrow$ So, area of parallelogram ABCD with height $DE$ and base$AB$ is,

$\Rightarrow$ Area of parallelogram $ABCD$ =$\frac{1}{2}\times AB\times DE$

$\Rightarrow$ $\frac{1}{2}\times 6\times 4$ [From ( 1 )]

$\therefore$ Area of parallelogram $ABCD=12c{m}^2$ ----- ( 2 )

$\Rightarrow$ In figure $BF\perp AD$

$\Rightarrow$ So now we can take BF as a height and AD as a base.

$\Rightarrow$ Area of parallelogram $ABCD=\frac{1}{2}\times AD\times BF$

$\Rightarrow$ $12=\frac{1}{2}\times 3\times BF$ [From ( 1 ) and ( 2 )]

$\Rightarrow$ $BF=\frac{24}{3}$

$\therefore$ $BF=8cm$