ABCD is a parallelogram. DE is perpendicular to AB, AB = 30cm, DE = 15cm and BC = 25cm. Find the length of DF, where DF is perpendicular to BC.

Answer :

We have ABCD is a parallelogram  , DE perpendicular to AB  ,
AB  = 30 cm
DE  =  15 cm
And
BC  =  25 cm

We know area of parallelogram  =  Base $\times$ Height 

And we take AB as base so DE is height of parallelogram ABCD 
So,
Area of ABCD  = 30  $\times$  15   =  450   cm²                      --------------- (  1 )

And  as give DF is perpendicular on BC , SO if we take BC as base , so DF is height  of parallelogram ABCD

And 
Area of ABCD  =  25 $\times$ DF                                     ----------------- ( 2 )

Now we equate equation 1 and 2 and get

25 $\times$ DF  =  450 

DF  = $\frac{450}{25}$  =  18  cm                                         (  Ans )