Question

Given: △ABC, E∈ AB m∠ABC=m∠ACE AB=34, AC=20 Find: AE

Answer 1

Answer:

The length of AE is 11.8 units.

Step-by-step explanation:

Given the triangle ABC, E∈ AB m∠ABC=m∠ACE AB=34, AC=20. we have to find the length of side AE.

In ΔACE and ΔABC

∠A=∠A     (Common)

∠ABC=∠ACE     (Given)

∴ By AA similarity, ΔACE is similar to ΔABC

Hence by triangle proportionality theorem,

$\frac{CE}{BC}=\frac{AE}{AC}=\frac{AC}{AB}$

⇒ $\frac{AE}{AC}=\frac{AC}{AB}$

⇒ $\frac{AE}{20}=\frac{20}{34}$

⇒  $AE=\frac{20}{34}\times 20=\frac{400}{34}=11.8units$