Answer:
[tex]DF = 38[/tex]
Step-by-step explanation:
Given
[tex]DE = 2x[/tex]
[tex]EF = 2x - 6[/tex]
[tex]DF = 3x + 5[/tex]
Required
Determine EF
Since E lies on DF, then
[tex]DF = DE + EF[/tex]
Substitute values for DF, DE and EF
[tex]3x + 5 = 2x + 2x -6[/tex]
Collect Like Terms
[tex]3x -2x -2x = -6 -5[/tex]
[tex]-x = -11[/tex]
Solve for x
[tex]x = 11[/tex]
Recall that
[tex]DF = 3x + 5[/tex]
Substitute 11 for x
[tex]DF = 3 * 11 + 5[/tex]
[tex]DF = 38[/tex]
