ANSWER:
( Option 3 ) = 18
The length of DF is equivalent to 18 units.
Explanation:
As HE is parallel to GF -
In Triangle DHE and Triangle DGF:
Angle DHE = Angle HGE ( equal corresponding angles on parallel lines )
Angle DEH = Angle EFG ( equal corresponding angles on parallel lines )
Angle HDE is a common angle in both triangles.
Therefore, Triangle DHE and Triangle DGF are similar triangles. ( Angle Angle Angle )
If Triangle DHE and Triangle DGF are similar triangles, then their sides must be proportional.
Therefore, in Triangle DHE and Triangle DGF:
DF : DE = DG : DH
DE = 6
DH = 4
DG = 4 + 8 = 12
DF = ?
THEREFORE:
DF : 6 = 12 : 4
DF : 6 = 3 : 1
DF = 3 × 6
DF = 18