Question

In triangle DEF M and N are mid points of sides EF and DE respectively if area triangle ENM = 4 cm sq find area triangle DEF

Answer 1

M and N are midpoints of sides EF and DE.

∴ 2MN = DF and MN║DF (Midpoint theorem) ... (1)

In ΔDEF and ΔMEN,

=> ∠DEF = ∠MEN (common angle)

=> ∠EFD = ∠ENM (corresponding angles)

∴ ΔDEF is similar ΔMEN (By AA test for similarity)

Ratio of sides = MN/DF = MN/2MN = 1/2 (From 1)

∴ Ratio of areas = (Ratio of sides)² = (1/2)² = 1/4

∴ 1/4 = Ar(ΔMEN)/Ar(ΔDEF)

=> 1/4 = 4/Ar(ΔDEF)

=> Ar(ΔDEF) = 4*4 = 16 sq.cm

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