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.

Answer 1

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.