Answer:
DG is 8.75.
Explanation:
Because we have an isosceles triangle with a perpendicular bisector, we have two identical triangles which share equal sides. We know DF is 14 and FG is 4x. These are corresponding sides and we set them equal.
4x=14
x= 3.5.
We also know DE=EG and that DE=1.25x.
We substitute this term and x=3.5.
1.25x=EG
1.25(3.5)=EG
EG is 4.375.
We double 4.375 to find the whole segment DG since they are equal halves. DG is 8.75.