Answer:
x = 6.6 units
Length of DE = 16.2 units
Step-by-step explanation:
Notice that they give you a proportion between sides of triangles based in the similarity of these two triangles CFD, and DEF
The proportion can be written as:
[tex]\frac{5}{9} = \frac{9}{2x+3} \\2x+3= \frac{9\,*\,9}{5}\\ 2x+3=\frac{81}{5} \\2x=\frac{81}{5} -3\\2x=\frac{81}{5} -\frac{15}{5} \\2x=\frac{66}{5} \\x=\frac{66}{10} \\x=6.6[/tex]
and therefore, the length of the segment DE becomes:
[tex]DE=2x+3\\DE=2(6.6)+3\\DE=13.2+3\\DE=16.2[/tex]
