Answer:
[tex]AE=20\ units[/tex]
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
Triangles AEB and DEC are similar by AA Similarity Theorem
so
[tex]\frac{AB}{DC}=\frac{AE}{DE}[/tex]
substitute the given values and solve for x
[tex]\frac{10}{4}=\frac{2x+10}{x+3}[/tex]
Multiply in cross
[tex]10x+30=8x+40\\10x-8x=40-30\\2x=10\\x=5[/tex]
Find the length side AE
[tex]AE=2x+10[/tex]
substitute the value of x
[tex]AE=2(5)+10=20\ units[/tex]
