Question

D and E are points on the sides AB and AC respectively of a ΔABC such that DE║BC.

If AB = 13.3cm, AC = 11.9cm and EC = 5.1cm, find AD.

Answer 1

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

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

Adding 1 to both sides, we get :

`(AD)/(DB) +1= (AE)/(EC) + 1`

⟹ `(AB)/(DB) = (AC)/(EC)`

⟹ `13.3/(DB) = (11.9)/(5.1)`

⟹ `DB = (13.3 × 5.1)/11.9  =5.7 cm`

Therefore, AD=AB-DB=13.5-5.7=7.6 cm