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Question
In a ∆ABC, D, E and F are, respectively, the mid-points of BC, CA and AB. If the lengths of side AB, BC and CA are 7 cm, 8 cm and 9 cm, respectively, find the perimeter of ∆DEF.
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Solution
Given that
AB = 7cm, BC = 8cm, AC = 9cm .
In ΔABC
∴ F and E are the midpoint of AB and AC
∴EF = `1/2` BC [Mid-points theorem]
Similarly
DF = `1/2` AC, DE = `1/2` AB
Perimeter of ΔDEF = 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 = 12cm
∴ Perimeter of ΔDEF = 12cm
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