Question

what is the value of p?
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Explanation:

Step1: Use the property of congruent triangles

Since \( \angle TSU=\angle RSU = 44^{\circ}\), \( \angle T=\angle R = 90^{\circ}\), and \( SU = SU\) (common side), by the AAS (Angle - Angle - Side) congruence criterion, \(\triangle TSU\cong\triangle RSU\).

Step2: Set up the equation based on congruent sides

For congruent triangles \(\triangle TSU\) and \(\triangle RSU\), the corresponding sides \(TU\) and \(RU\) are equal. So we have the equation \(7p=p + 48\).

Step3: Solve the equation for \(p\)

Subtract \(p\) from both sides of the equation \(7p=p + 48\):
\(7p-p=p + 48-p\)
\(6p=48\)
Divide both sides by 6: \(p=\frac{48}{6}\)

Answer:

\(8\)