Question

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

Answer 1

In Δ ABC, it is given that DE ∥ BC.
Applying Thales’ theorem, we get:

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

∵ AD = 3.6 cm , AB = 10 cm, AE = 4.5cm
∴ DB = 10 − 3.6 = 6.4cm

Or,`(3. 6) /(6.4)=(4.5)/(EC)`

Or, EC =`(6. 4× 4.5)/3.6`

Or, EC= 8 cm
Thus, AC = AE + EC
= 4.5 + 8 = 12.5 cm