Question

if ( rs = st = 28 ), ( ru = 2p ), and ( tu = p + 11 ), what is the value of ( p )?

Explanation:

Step1: Use the perpendicular bisector theorem

Since \(RS = ST = 28\) and \(SU\) is perpendicular to \(RT\), by the perpendicular bisector theorem, \(RU=TU\).

Step2: Set up the equation

We know that \(RU = 2p\) and \(TU=p + 11\). So, \(2p=p + 11\).

Step3: Solve the equation for \(p\)

Subtract \(p\) from both sides of the equation \(2p=p + 11\).
\(2p-p=p + 11-p\)
\(p = 11\)

Answer:

\(11\)