Question

find $rs$. explain your reasoning.
$rs = \square$
the answer can be found by using the

Explanation:

Step1: Apply Angle Bisector Theorem

Since \( SQ \) is the angle bisector and \( SP\perp QP\), \( SR\perp QR\), by the Angle Bisector Theorem, \( SP = SR\). So \(6x + 5=9x - 4\).

Step2: Solve for \(x\)

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Step3: Find \(RS\)

Substitute \(x = 3\) into \(9x-4\). Then \(RS=9\times3 - 4=27-4 = 23\).

Answer:

\(RS = 23\)