Answer:
Part 1) [tex]x=6.6\ units[/tex]
Part 2) [tex]DE=16.2\ units[/tex]
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
[tex]CD/FD=FD/DE[/tex]
[tex]\frac{5}{9}=\frac{9}{2x+3} \\ \\5*(2x+3)=9*9\\ \\10x+15=81\\ \\10x= 81-15\\ \\10x=66\\ \\ x=6.6\ units[/tex]
Part 2) Find the length of DE
[tex]DE=2x+3[/tex]
substitute the value of x
[tex]DE=2(6.6)+3=16.2\ units[/tex]
