The value of DE + EF is 13
Congruent triangles are triangles with equal corresponding angles and equal corresponding side lengths.
Since triangle ABD is congruent to triangle CEF then;
line EF = BD
line CF = AD
line AB = CE
If the perimeter of ABD = 27
BD = 27 - ( 7 + 9)
BD = 27 - 16
BD = 11
CD = 11 - 6 = 5
DE = CE - CD
DE = 7 - 5
= 2
Therefore;
EF = BD
The value of DE + EF
= 2 + 11
= 13