Question

solve it fast.....................

Answer 1

Answer:

The figure is in the attachment

Given

D ,E and F are the mid points of AB,BC and AC respectively

By midpoint theorem

DE =1/2AC

EF =1/2AB

DF =1/2 BC

=>DE=AF

  EF=AD and DF=BE-(1)

In ABC and ADF

AD/AB=AE/AC=DF/BC-(2)

By SSS similarity criteria,

  ABC~ADF

Subs (1) in (2),

=>EF/AB=DE/AC=DF/BC

By SSS similarity criteria ,

  DEF~ABC

Now,

ar(DEF)/ar(ABC)=(DE/AC)^2

                     =(1/2AC/AC)^2

                          =(1/2)^2

                      =1/4

Therefore,

  A(DEF):A(ABC)=1:4

Here,

‘A or ar means area’

     Thank you