Question:
In ΔABC, D, E and F are, respectively the mid points of BC, CA and AB. If the lengths of sides AB, BC and CA are 7cm, 8 cm and 9 cm, respectively, find the perimeter of ΔDEF.
Solution:
Given that,
AB = 7 cm, BC = 8 cm, AC = 9 cm
In ∆ABC,
F and E are the mid points of AB and AC.
∴ EF = 1/2 BC
Similarly
DF = 1/2 AC and DE = 1/2 AB
Perimeter of ∆DEF = DE + EF + DF
= (1/2) AB + (1/2) BC + (1/2) AC
= 1/2 ∗7 + 1/2 ∗8 + 1/2 ∗9
= 3.5 + 4 + 4.5
= 1/2 cm
Perimeter of ΔDEF = 1/2 cm
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