Question

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

Answer 1

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:

$3(3x - 1) = \frac{1}{2}*5(2x + 2)$

Solve for x

$9x - 3 = \frac{5}{2}(2x + 2)$

Multiply both sides by 2

$2(9x - 3) = \frac{5}{2}(2x + 2)*2$

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

$18x - 6 = 10x + 10$

$18x - 10x = 6 + 10$

$8x = 16$

Divide both sides by 8

$x = 2$

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

Plug in the value of x

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

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

$AC = 5(2x + 2)$

$AC = 5(2(2) + 2)$

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