Since m is the midpoint of ab, then the following relationship is fulfilled:
[tex]am = \frac{ab}{2} [/tex]
Therefore, substituting values we have:
[tex]2x+9 = \frac{8x-50}{2} [/tex]
From here, we clear the value of x.
We have then:
[tex]2x+9 = 4x-25 [/tex]
[tex]9+25 = 4x-2x [/tex]
[tex]34 = 2x [/tex]
[tex]x = \frac{34}{2} [/tex]
[tex]x = 17 [/tex]
Then, the value of am, is given by substituting x in the expression:
[tex]am=2x+9[/tex]
Substituting we have:
[tex]am=2(17)+9[/tex]
[tex]am=34+9[/tex]
[tex]am=43[/tex]
Answer:
the length of am is:
[tex]am=43[/tex]
