Question

If B is the midpoint of AC, solve for x, and find the lengths of AB, BC, and AC.

Please show all work and not just the answers.

Answer 1

x = 2

AB = 15

BC = 15

AC = 30

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:

`3(3x - 1) = (1)/(2)*5(2x + 2)`

Solve for x

`9x - 3 = (5)/(2)(2x + 2)`

Multiply both sides by 2

`2(9x - 3) = (5)/(2)(2x + 2)*2`

`18x - 6 = 5(2x + 2)`

`18x - 6 = 10x + 10`

`18x - 10x = 6 + 10`

`8x = 16`

Divide both sides by 8

`x = 2`

`AB = BC = 3(3x - 1)`

Plug in the value of x

`AB = BC = 3(3(2) - 1)`

`= 3(6 - 1) = 3(5) = 15`

`AC = 5(2x + 2)`

`AC = 5(2(2) + 2)`

`AC = 5(4 + 2) = 5(6) = 30`