Question

8. In a ∆ABC, D, E, F are, respectively, the mid-points of BC, CA and AB. If the lengths of sides AB, BC and CA are 17 cm, 18 cm and 19 cm respectively, find the perimeter of ∆DEF.​​

Answer 1

Step-by-step explanation:

Since, D,E,F are the midpoints of BC,CA and AB,Thus

DE

AB

=

EF

BC

=

DF

AC

=2

△ABC∼△DEF

Now,

Perimeter of △DEF=DE+EF+DF

=

2

AB

+

2

BC

+

2

AC

=

2

7

+

2

8

+

2

9

=

2

7+8+9

=

2

24

=12 cm.