Part 1) ![x=6.6\ units](/tpl/images/0502/3361/35074.png)
Part 2) ![DE=16.2\ units](/tpl/images/0502/3361/79b53.png)
Step-by-step explanation:
Part 1) Find the value of x
we know that
Triangles CDF and FDE are similar
therefore
The ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
![CD/FD=FD/DE](/tpl/images/0502/3361/95081.png)
![\frac{5}{9}=\frac{9}{2x+3} \\ \\5*(2x+3)=9*9\\ \\10x+15=81\\ \\10x= 81-15\\ \\10x=66\\ \\ x=6.6\ units](/tpl/images/0502/3361/b5300.png)
Part 2) Find the length of DE
![DE=2x+3](/tpl/images/0502/3361/58148.png)
substitute the value of x
![DE=2(6.6)+3=16.2\ units](/tpl/images/0502/3361/f955e.png)