Question

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

StartFraction 5 Over 9 EndFraction = StartFraction 9 Over 2 x + 3 EndFraction
10x + 15 = 9(9)

x =

Length of DE = ___ units

Answer 1

StartFraction 5 Over 9 EndFraction = StartFraction 9 Over 2 x + 3 EndFraction

10x + 15 = 9(9)

x = 6.6

Length of = 16.2 units

Explanation:

Answer 2

x = 6.6 units

Length of DE = 16.2 units

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:

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

and therefore, the length of the segment DE becomes:

`DE=2x+3\\DE=2(6.6)+3\\DE=13.2+3\\DE=16.2`