Question

applying the perpendicular bisector theorem
what is the length of segment sr?
units

Explanation:

Step1: Apply the Perpendicular Bisector Theorem

Since line \(l\) is the perpendicular bisector of \(RQ\), by the Perpendicular Bisector Theorem, \(SR = SQ\). So, \(2x + 8=8x - 4\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(8 = 6x-4\).
Add \(4\) to both sides: \(12 = 6x\).
Divide both sides by \(6\): \(x = 2\).

Step3: Find the length of \(SR\)

Substitute \(x = 2\) into \(2x + 8\). So, \(SR=2\times2 + 8\).
Calculate: \(SR = 4 + 8=12\).

Answer:

\(12\)