Question

In AABC, point D is the centroid, and AD= 12. Find AG

Answer 1

AG = 18

Explanation:

The relationship of the segments created is one is 1/3 (shorter) and the other (longer) is 2/3 of the total length.

Lets make x represent AG.

So, 2/3 of x is 12

or

`(2)/(3)`x = 12

Multiply both sides by the reciprocal of
`(2)/(3)` , which is
`(3)/(2)`.

(
`(3)/(2)`)
`(2)/(3)`x = 12 (
`(3)/(2)`) (x is left alone, the fractions = 1 when multiplied)

x = 12 (
`(3)/(2)`) ( 12 times 3 = 36, divided by 2 = 18)

x = 18

Answer 2

The calculated length of the segment AG is 18 units

How to determine the length of the segment AG

From the question, we have the following parameters that can be used in our computation:

The triangle

Also, we have

The point D is the centroid

AD = 12

This means that

AD : GD = 2 : 1

So, we have

AD/GD = 2

Substitute the known values into the equation

12/GD = 2

We have

GD = 12/2

Evaluate

GD = 6

Next, we have

AG = 6 + 12

AG = 18

Hence, the length of the segment AG is 18 units