Answer:
[tex]x=9.5\ units[/tex]
Step-by-step explanation:
The complete question is
Segment BC is parallel to segment DE. Find the value of x
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In his problem
Triangle ABC is similar to Triangle ADE by AA Similarity Theorem
so
[tex]\frac{AB}{AD}=\frac{AC}{AE}[/tex]
substitute the given values
[tex]\frac{x+3+x-2}{x-2}=\frac{5+3}{3}[/tex]
solve for x
[tex]\frac{2x+1}{x-2}=\frac{8}{3}[/tex]
[tex]6x+3=8x-16\\8x-6x=3+16\\2x=19\\x=9.5[/tex]
