Question

In ΔABC, D and E are the mid-point on AB and AC such that DE || BC.
If AD : BD = 4 : 5 and EC = 2.5cm, find AE.

Answer 1

In ΔADE and ΔABC
∠D = ∠B and ∠C = ∠E   ...(DE || BC)
⇒ ΔADE ∼ ΔABC

∴ `"AD"/"DB" = "AE"/"EC"`

⇒ `(4)/(5) = "AE"/(2.5)`

⇒ AE = `(4 xx 2.5)/(5)`
⇒ AE = 2cm.