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prohojiy [21]
3 years ago
14

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

Mathematics
1 answer:
const2013 [10]3 years ago
7 0

Answer:

DG = 26

GE = 26

DF = 15

CH = 14

CE = 28

Step-by-step explanation:

The figure has been attached, to complement the question.

DE = 52

FC = 15

HE = 14

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:

DF = FC

CH = HE

DG = GE

Solving (a): DG

If DG = GE, then

DE = DG + GE

DE = DG + DG

DE = 2DG

Make DG the subject

DG = \frac{1}{2}DE

Substitute 52 for DE

DG = \frac{1}{2} * 52

DG = 26

Solving (b): GE

If DG = GE, then

GE = DG

GE = 26

Solving (c): DF

DF = FC

So:

DF = 15

Solving (d): CH

CH = HE

CH = 14

Solving (e): CE

If CH = HE, then

CE = CH + HE

CE = 14 + 14

CE = 28

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