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.
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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.
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