Answer:
Option B [tex]2\frac{2}{3}\ units[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
Triangles ABC and ADE are similar by AA Similarity Theorem
so
[tex]\frac{AB}{AD}=\frac{AC}{AE}[/tex]
substitute the given values
[tex]\frac{3}{3+2}=\frac{4}{AE}[/tex]
Solve for AE
[tex]\frac{3}{5}=\frac{4}{AE}[/tex]
[tex]AE=5(4)/3[/tex]
[tex]AE=\frac{20}{3}\ units[/tex]
Find the length of CE
[tex]AE=AC+CE\\CE=AE-AC[/tex]
substitute the values
[tex]CE=\frac{20}{3}-4[/tex]
[tex]CE=\frac{8}{3}\ units[/tex]
Convert to mixed number
[tex]\frac{8}{3}\ units=\frac{6}{3}+\frac{2}{3}=2\frac{2}{3}\ units[/tex]
