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If J is the centroid of cde, de=52, fc=15, he=14, find each missing measure

Sagot :

MrRoyal

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]

View image MrRoyal
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