D and E are points on the sides AB and AC respectively of a ΔABC such that DE || BC. If AD = 3.6 cm, AB = 10 cm and AE = 4.5 cm, find EC and AC.

Question

Philoid · Accepted Answer

Given: AD = 3.6 cm, AB = 10 cm and AE = 4.5 cm.

Applying Thale’s Theorem,

⇒

⇒ [∵ DB = AB – AD ⇒ DB = 10 – 3.6 = 6.4]

⇒

⇒ EC = 8

Now, AC = AE + EC

⇒ AC = 4.5 + 8 = 12.5

Hence, EC = 8 cm and AC = 12.5 cm