Answer
10) x = 13 units
11) AB = 270 units
Step-by-step explanation
The line segment PQ bisects the AB. And we were told that
AC = (9x + 18)
CB = (12x - 21)
But if the line segment PQ bisects the line AB, it means that AC will be equal to CB.
AC = CB
(9x + 18) = (12x - 21)
We can rewrite this as
12x - 21 = 9x + 18
12x - 9x = 18 + 21
3x = 39
Divide both sides by 3
(3x/3) = (39/3)
x = 13 units.
But question 11 asks us to calculate the length of AB
AB = AC + CB
AB = 9x + 18 + 12x - 21
AB = 21x - 3
Substituting 13 for x
AB = (21 × 13) - 3
AB = 273 - 3 = 270 units.
Hope this Helps!!!