Question

In the diagram below of ABC below,AB is extended to point D. what is m

Answer 1

Given that C is the centroid of the triangle, then:

`(QC)/(CM)=2`

This means that the length of QC is twice the length of CM.

Substituting with QC = 5x and CM = x + 12, and solving for x:

`\begin{gathered} (5x)/(x+12)=2 \\ 5x=2\cdot(x+12) \\ 5x=2x+2\cdot12 \\ 5x-2x=24 \\ 3x=24 \\ x=(24)/(3) \\ x=8 \end{gathered}`

The length of QM can be expressed as follows:

QM = QC + CM

Substituting with QC = 5x and CM = x + 12

QM = 5x + x + 12

QM = 6x + 12

Substituting with x = 8:

QM = 6*8 + 12

QM = 48 + 12

QM = 60