Question

applying the perpendicular bisector theorem. what is the length of segment sr? units. r t q 2x + 8 8x - 4 s

Explanation:

Step1: Apply 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: \(8 = 8x-2x - 4\), which simplifies to \(8 = 6x - 4\). Then add 4 to both sides: \(8 + 4=6x\), so \(12 = 6x\). Divide both sides by 6, we get \(x = 2\).

Step3: Find the length of \(SR\)

Substitute \(x = 2\) into the expression for \(SR\): \(SR=2x + 8\). Then \(SR=2\times2 + 8=4 + 8 = 12\).

Answer:

12