The length of both line segment DE and EF is 14 units and the length of the DF line segment is 28 units.
Given:
A line segment DF with midpoint E.
DE = 2x+4
EF = 3x-1
To find:
The lengths of all segemnt
Solution:
E is the midpoint of line segment DF which means line DF is divided into two equal line segments DE and EF.
[tex]DF = EF\\2x+4 = 3x-1[/tex]
Solving for x:
[tex]4+1=3x-2x\\5=x\\x=5[/tex]
The length of the DE line segment :
[tex]DE = 2x+4 = 2\times 5+4 = 14[/tex]
The length of the EF line segment:
[tex]EF=3x-1 = 3\times 5-1 = 14[/tex]
The length of the DF segment:
[tex]DF= DE+EF= 14+14 =28[/tex]
The length of both line segment DE and EF is 14 units and the length of the DF line segment is 28 units.
Learn more about midpoints and line segments here:
brainly.com/question/7826311?referrer=searchResults
