Question

5.1 assignment
2 of 22
possible points: 0.45
algebra find the length of \\( \overline{ab} \\).
diagram: triangle with point a, and two segments ac (labeled 3x - 6) and ab (labeled x + 18), and a perpendicular segment from c to ab at d, with d marking equal segments on cb (indicated by red marks).
ab = \\( \boxed{} \\) units

Explanation:

Step1: Set up the equation

Since \(AD\) is the perpendicular bisector of \(CB\), \(AC = AB\). So, \(3x - 6=x + 18\).

Step2: Solve for \(x\)

Subtract \(x\) from both sides: \(3x-x-6=x - x+ 18\), which simplifies to \(2x-6 = 18\).
Add \(6\) to both sides: \(2x-6 + 6=18 + 6\), so \(2x=24\).
Divide both sides by \(2\): \(x=\frac{24}{2}=12\).

Step3: Find the length of \(AB\)

Substitute \(x = 12\) into the expression for \(AB\) (\(x + 18\)). So, \(AB=12 + 18\).

Answer:

\(30\)