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Question
In ΔABC, D and E are the mid-point on AB and AC such that DE || BC.
If AD = 4, AE = 8, DB = x - 4 and EC = 3x - 19, find x.
Solution
In ΔADE and ΔABC
∠D = ∠B and ∠C = ∠E ...(DE || BC)
⇒ ΔADE ∼ ΔABC
∴ `"AD"/"DB" = "AE"/"EC"`
⇒ `(4)/(x - 4) = (8)/(3x - 19)`
⇒ 4 x (3x - 19) = 8x (x - 4)
⇒ 12x - 76 = 8x - 32
⇒ 4x = 44
⇒ x = 11.
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