Final answer:
By setting the expressions for BX (9x+6) and CX (3x+18) equal since AX bisects BC, we solve for x and find that BX is 24.
Step-by-step explanation:
In triangle ABC, AX is given as the perpendicular bisector of BC. This means point X is the midpoint of BC, so BX and CX are equal. Since BX is expressed as 9x+6 and CX is expressed as 3x+18, we can set these expressions equal to each other to find the value of x:
- 9x + 6 = 3x + 18
- 9x - 3x = 18 - 6
- 6x = 12
- x = 2
Now that we have the value of x, we can substitute it back into the expression for BX to find the length of BX:
- BX = 9x + 6
- BX = 9(2) + 6
- BX = 18 + 6
- BX = 24