x = 43, AB = 49, BC = 49 and AC =98.
Solution:
Given data:
AC = 3x - 31 and AB = x + 6
B is the midpoint of AC.
Therefore AB = BC .
BC = x + 6
AB + BC = AC
x + 6 + x + 6 = 3x - 31
2x + 12 = 3x - 31
Add 31 on both sides, we get
2x + 43 = 3x
Subtract 2x from both sides, we get
43 = x
AB = x + 6
= 43 + 6
AB = 49
BC = 49
AC = 3x - 31
= 3(43) - 31
= 129 - 31
AC = 98
Therefore x = 43, AB = 49, BC = 49 and AC =98.