In △DEF, G and H are points on side DE and DF respectively. GH is parallel to EF. If G divides DE in the ratio 1:3 and HF is 7.2cm, find the length of DF.

According to the Basic Proportionality Theorem (Thales's Theorem), since GH∥EF in △DEF:
GE
DG
​
=
HF
DH
​

Given that G divides DE in the ratio 1:3, we have:

GE
DG
​
=
3
1
​

Therefore:

3
1
​
=
7.2
DH
​

DH=
3
7.2
​
=2.4cm
The total length of DF is:

DF=DH+HF=2.4+7.2=9.6cm