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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.
Solution
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.
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