Question

if qr ≅ rs, qt = 5v - 41, and st = 2v - 8, what is the value of v?

Explanation:

Step1: Apply the perpendicular bisector theorem

Since \(QR = RS\) and \(RT\perp QS\), by the perpendicular bisector theorem, \(QT = ST\).

Step2: Set up the equation

Set \(5v - 41=2v - 8\).

Step3: Solve for \(v\)

Subtract \(2v\) from both sides: \(5v-2v - 41=2v-2v - 8\), which simplifies to \(3v-41=-8\).
Add \(41\) to both sides: \(3v-41 + 41=-8 + 41\), so \(3v = 33\).
Divide both sides by \(3\): \(v=\frac{33}{3}=11\).

Answer:

\(11\)