Question

In the adjoining figure D,E,f are the mid – points of the sides AB ,BC and CA

respectively

i) If AC = 7.4 cm, find DE​

Answer 1

Answer:

AB=6 cm,BC=4.8 cm and CA=5.6 cm

D,E and F are the mid points of sides BC,CA and AB of △ABC

To find: The perimeter of △DEF

Given,

E and F are the midpoints of sides CA and AB

⇒AE=EC and AF=FD

∴

EC

AE

=

FB

AF

⇒EF=

2

1

BC[ By mid point theorem ]

⇒EF=

2

1

×4.8=2.4 cm

Similarly,

DE=

2

1

AB=

2

1

×6=3 cm

FD=

2

1

AC=

2

1

×5.6=2.8 cm

∴ Perimeter of △DEF=DE+EF+FD

=3+2.4+2.8

=8.2 cm