Answer:
AE = 11.76 units
Step-by-step explanation:
For better understanding of the solution, see the attached figure :
Given : E ∈ AB, m∠ABC = m∠ACE, AB = 34 and AC = 20
To find AE :
In ΔABC and ΔACE,
m∠ABC = m∠ACE ( Given )
∠A = ∠A ( Common angle for both the triangles )
By AA postulate of similarity of triangles, ΔABC ~ ΔACE
So, proportion of the corresponding will be equal.
[tex]\implies \frac{AC}{AB}=\frac{CE}{BC}=\frac{AE}{AC}\\\\\implies\frac{AC}{AB}=\frac{AE}{AC}\\\\\implies\frac{20}{34}=\frac{AE}{20}\\\\\implies AE=\frac{20\times 20}{34}\approx 11.76[/tex]
Hence, AE = 11.76 units
