Answer: 10.5 units
Step-by-step explanation:
Basic proportionality theorem says that if a line is drawn parallel to one side of a triangle intersecting the other two sides then it divides the two sides in the same ratio.
In the given triangle DEF , Line segment GH is drawn parallel to segment EF also GH is intersecting the other two sides ED and FH at G and H respectively.
GE= 6 units , DH = 14 units , HF = 8 units.
Then by Basic proportionality theorem , we have
[tex]\dfrac{DG}{GE}=\dfrac{DH}{HF}\\\\\Rightarrow\dfrac{DG}{6}=\dfrac{14}{8}\\\\\Rightarrow\ DG=\dfrac{14}{8}\times6=10.5[/tex]
Hence, the length of Line segment GD = 10.5 units.
