Question

What is the value of x and the length of segment DE?

10x + 15 = 9(9)
x =

Length of =
units

Answer 1

x = 6.6

Length of = 16.2 units

Answer 2

Part 1)
`x=6.6\ units`

Part 2)
`DE=16.2\ units`

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`

`(5)/(9)=(9)/(2x+3) \\ \\5*(2x+3)=9*9\\ \\10x+15=81\\ \\10x= 81-15\\ \\10x=66\\ \\ x=6.6\ units`

Part 2) Find the length of DE

`DE=2x+3`

substitute the value of x

`DE=2(6.6)+3=16.2\ units`