Answer: [tex]QM=20[/tex]
Step-by-step explanation:
1. By definition, the midpoint is the point of a segment where it is divided into two equal segments.
2. Keeping the definition above on mind, if [tex]QM=16+x[/tex] and [tex]MR=2(2x+2)[/tex], you can calculate the lenght of [tex]QM[/tex] as following:
- Equal both equations:
[tex]16+x=2(2x+2)[/tex]
- Solve for [tex]x[/tex]:
[tex]16+x=2(2x+2)\\16+x=4x+4\\16-4=4x-x\\12=3x\\x=4[/tex]
- Substitute the value of [tex]x[/tex] into [tex]QM=16+x[/tex]:
[tex]QM=16+4=20[/tex]
