Question

if ( rs = ru = 60 ), ( st = 3p ), and ( tu = p + 56 ), what is the value of ( p )?

Explanation:

Step1: Use the Hypotenuse - Leg (HL) Congruence Theorem

Since \(RS = RU = 60\) and \(RT\) is a common side (\(RT=RT\)) and \(\angle SRT=\angle URT = 90^{\circ}\), by the HL (Hypotenuse - Leg) Congruence Theorem, \(\triangle SRT\cong\triangle URT\).

Step2: Set up the equation based on congruent triangles

If \(\triangle SRT\cong\triangle URT\), then \(ST = TU\) (corresponding parts of congruent triangles are equal).
We know that \(ST = 3p\) and \(TU=p + 56\). So, we set up the equation \(3p=p + 56\).

Step3: Solve the equation for \(p\)

Subtract \(p\) from both sides of the equation \(3p=p + 56\):
\(3p-p=p + 56-p\)
\(2p=56\)
Divide both sides by 2: \(p=\frac{56}{2}\)

Answer:

\(28\)