Question

In ΔABC, D and E are the mid-point on AB and AC such that DE || BC.
If AD = 8cm, AB = 12cm and AE = 12cm, find CE.

Answer 1

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

∴ `"AD"/"DB" = "AE"/"EC"`

DB
= AB - AD
= 12 - 8
= 4

⇒ `(8)/(4) = (12)/"EC"`

⇒ 8 x EC = 12 x 4

⇒ EC = `(12 xx 4)/(8)`
⇒ EC = 6cm.