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ANSWER:

( Option 3 ) = 18

The length of DF is equivalent to 18 units.

STEP-BY-STEP 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
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