Answer:
x = 2
AB = 15
BC = 15
AC = 30
Step-by-step explanation:
Given that B is the midpoint of AC, then AB = ½ of AC.
AB is given as 3(3x - 1),
AC = 5(2x + 2),
Therefore:
[tex] 3(3x - 1) = \frac{1}{2}*5(2x + 2) [/tex]
Solve for x
[tex] 9x - 3 = \frac{5}{2}(2x + 2) [/tex]
Multiply both sides by 2
[tex] 2(9x - 3) = \frac{5}{2}(2x + 2)*2 [/tex]
[tex] 18x - 6 = 5(2x + 2) [/tex]
[tex] 18x - 6 = 10x + 10 [/tex]
[tex] 18x - 10x = 6 + 10 [/tex]
[tex] 8x = 16 [/tex]
Divide both sides by 8
[tex] x = 2 [/tex]
[tex] AB = BC = 3(3x - 1) [/tex]
Plug in the value of x
[tex] AB = BC = 3(3(2) - 1) [/tex]
[tex] = 3(6 - 1) = 3(5) = 15 [/tex]
[tex] AC = 5(2x + 2) [/tex]
[tex] AC = 5(2(2) + 2) [/tex]
[tex] AC = 5(4 + 2) = 5(6) = 30 [/tex]
