Answer:
[tex]DG = 26[/tex]
[tex]GE = 26[/tex]
[tex]DF = 15[/tex]
[tex]CH = 14[/tex]
[tex]CE = 28[/tex]
Step-by-step explanation:
The figure has been attached, to complement the question.
[tex]DE = 52[/tex]
[tex]FC = 15[/tex]
[tex]HE = 14[/tex]
Given that J is the centroid, it means that J divides sides CD, DE and CE into two equal parts respectively and as such the following relationship exist:
[tex]DF = FC[/tex]
[tex]CH = HE[/tex]
[tex]DG = GE[/tex]
Solving (a): DG
If [tex]DG = GE[/tex], then
[tex]DE = DG + GE[/tex]
[tex]DE = DG + DG[/tex]
[tex]DE = 2DG[/tex]
Make DG the subject
[tex]DG = \frac{1}{2}DE[/tex]
Substitute 52 for DE
[tex]DG = \frac{1}{2} * 52[/tex]
[tex]DG = 26[/tex]
Solving (b): GE
If [tex]DG = GE[/tex], then
[tex]GE = DG[/tex]
[tex]GE = 26[/tex]
Solving (c): DF
[tex]DF = FC[/tex]
So:
[tex]DF = 15[/tex]
Solving (d): CH
[tex]CH = HE[/tex]
[tex]CH = 14[/tex]
Solving (e): CE
If [tex]CH = HE[/tex], then
[tex]CE = CH + HE[/tex]
[tex]CE = 14 + 14[/tex]
[tex]CE = 28[/tex]
