Question

practice 35

1. find ( qp ).

( qp=square )
explain your reasoning.

Explanation:

Step1: Use the Angle - Bisector Theorem

Since \(QS\) is the angle bisector of \(\angle PSR\) and \(QP\perp PS\), \(QR\perp SR\), by the Angle - Bisector Theorem, \(QP = QR\). So \(6x=3x + 9\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides of the equation \(6x=3x + 9\). We get \(6x-3x=3x + 9-3x\), which simplifies to \(3x=9\). Then divide both sides by \(3\): \(x=\frac{9}{3}=3\).

Step3: Find the length of \(QP\)

Substitute \(x = 3\) into the expression for \(QP\) (which is \(6x\)). So \(QP=6\times3 = 18\).

Answer:

\(18\)