Question

find the length of \\( \overline { a b } \\).
3.
4.

Explanation:

Problem 3

Step1: Use the property of congruent segments

Since \(BD\) is the perpendicular bisector of \(AC\), by the perpendicular bisector theorem, \(AB = BC\). So, \(3x + 8=7x - 16\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(8 = 4x-16\).
Add \(16\) to both sides: \(24 = 4x\).
Divide both sides by \(4\): \(x = 6\).

Step3: Find the length of \(AB\)

Substitute \(x = 6\) into \(AB=3x + 8\).
\(AB=3\times6 + 8=18 + 8=26\).

Step1: Use the property of congruent segments

Since \(BD\) is the perpendicular bisector of \(AC\), by the perpendicular bisector theorem, \(BC = AB\). So, \(6x+11 = 11x - 9\).

Step2: Solve the equation for \(x\)

Subtract \(6x\) from both sides: \(11 = 5x-9\).
Add \(9\) to both sides: \(20 = 5x\).
Divide both sides by \(5\): \(x = 4\).

Step3: Find the length of \(BC\) (or \(AB\))

Substitute \(x = 4\) into \(BC = 6x+11\).
\(BC=6\times4+11=24 + 11=35\).

Answer:

\(26\)

Problem 4