Question

If G is the centroid of triangle ACE, AG = 8, GF = 7, BG = 5, find each measure.

Answer 1

The measure of each length is given below as follows:

GD= 4

AD= 12

CG= 14

GE= 10

BE= 15

How to calculate the measure of the missing lengths?

To calculate the measure of the given lengths, the following steps should be taken as follows:

Given that ;

G is the centroid of triangle ACE, the formula to be used;

CG:GF = 2:1

Given,

AG = 8,

GF = 7,

BG = 5,

For GD:

AG:GD = 2:1

8:GD=2:1

GD=8÷2= 4

For AD:

AD = AG+GD

= 8+4= 12

For CG:

CG:GF = 2:1

CG:7 = 2:1

CG = 7×2=14

For GE;

GE:BG =2:1

GE:5 =2:1

GE= 2×5/1

= 10

For BE:

BE = BG+GE

5+10 = 15

Answer 2

Answer:

GD = 4

AD = 12

CG = 14

GE = 10

BE = 15

Step-by-step explanation:

Because G is the centroid, then the following are correct

CG : GF = 2 : 1

AG : GD = 2 : 1

GE : BG = 2 : 1

So to find

GD, given AG = 8, we have:

8/GD = 2/1

GD = 8/2 = 4

AD = AG + GD

= 8 + 4

= 12

CG/GF = 2/1

CG/7 = 2/1

CG = 14

GE/BG = 2/1

GE/5 = 2/1

GE = 10

BE = GE + BG

= 10 + 5

= 15