Question

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

Answer 1

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

$CE = CH + HE$

$CE = 14 + 14$

$CE = 28$