Answer:
[tex]AE=20\ units[/tex]
Step-by-step explanation:
we know that
If AB is parallel to CD
then
triangles ABE and EDC are similar
Remember that
If two triangles are similar
then
the ratio of their corresponding sides is equal and their corresponding angles are equal too
In this problem
[tex]\frac{AE}{ED}=\frac{AB}{CD}[/tex]
substitute the values and solve for x
[tex]\frac{2x+10}{x+3}=\frac{10}{4}[/tex]
[tex]4(2x+10)=10(x+3)\\8x+40=10x+30\\10x-8x=40-30\\2x=10\\x=5\ units[/tex]
Find the length of AE
[tex]AE=2x+10[/tex] -----> substitute the value of x
[tex]AE=2(5)+10=20\ units[/tex]
