Question

what is qr?
s
27
6b - 57
t
27
r

b + 23
q
qr = \square

Explanation:

Step1: Use the property of perpendicular bisector

Since \(RT\) is the perpendicular bisector of \(SQ\) (given \(ST = TQ=27\)), then \(SR = QR\) (by the perpendicular bisector theorem). So, \(6b - 57=b + 23\).

Step2: Solve the equation for \(b\)

Subtract \(b\) from both sides: \(6b - b-57=b - b + 23\), which simplifies to \(5b-57 = 23\).
Add \(57\) to both sides: \(5b-57 + 57=23 + 57\), so \(5b=80\).
Divide both sides by \(5\): \(b=\frac{80}{5}=16\).

Step3: Find the length of \(QR\)

Substitute \(b = 16\) into the expression for \(QR\) (\(QR=b + 23\)). Then \(QR=16+23\).

Answer:

\(39\)