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,
[tex]\frac{CE}{BC}=\frac{AE}{AC}=\frac{AC}{AB}[/tex]
⇒ [tex]\frac{AE}{AC}=\frac{AC}{AB}[/tex]
⇒ [tex]\frac{AE}{20}=\frac{20}{34}[/tex]
⇒ [tex]AE=\frac{20}{34}\times 20=\frac{400}{34}=11.8units[/tex]
