Question

if ( qt = st = 42 ), ( qr = b + 44 ), and ( rs = 3b ), what is the value of ( b )?

Explanation:

Step1: Apply the perpendicular bisector theorem

Since \(QT = ST = 42\) and \(RT\perp SQ\), by the perpendicular bisector theorem, \(QR=RS\).

Step2: Set up the equation

We know that \(QR = b + 44\) and \(RS = 3b\). So, \(b + 44=3b\).

Step3: Solve the equation for \(b\)

Subtract \(b\) from both sides: \(44=3b - b\), which simplifies to \(44 = 2b\). Then divide both sides by \(2\): \(b=\frac{44}{2}\).

Answer:

\(22\)