1.

D and E are points on the sides AB and AC respectively of a ∆ABC such that DE || BC. If AD/DB = 4/7 and AC = 6.6 cm, find AE.

Answer»

From given triangle, points D and E are on the sides AB and AC respectively such that DE || BC.

AD/DB = 4/7 or AD = 4 cm, DB = 7 cm, and AC = 6.6

By Thale’s Theorem:

AD/DB = AE/EC

Add 1 on both sides

AD/DB + 1 = AE/EC + 1

(AD + DB)/DB = (AE + EC)/EC

(4+7)/7 = AC/EC = 6.6/EC

EC = (6.6 x 7)/11

= 4.2

And, AE = AC – EC

AE = 6.6 – 4.2

AE = 2.4 cm



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