Question

tifying a leg length
what is the length of \\( \overline { p r } \\)?
units

Explanation:

Step1: Identify the triangle type

Since \(\angle P=\angle Q\), \(\triangle PQR\) is an isosceles triangle. In an isosceles triangle, the sides opposite equal angles are equal. So \(PR = QR\).

Step2: Set up the equation

We know \(PR = 5n\) and \(QR=32 + n\). Then \(5n=32 + n\).

Step3: Solve the equation

Subtract \(n\) from both sides: \(5n - n=32 + n - n\), which gives \(4n = 32\).
Divide both sides by \(4\): \(n=\frac{32}{4}=8\).

Step4: Find the length of \(PR\)

Substitute \(n = 8\) into \(PR = 5n\). So \(PR=5\times8 = 40\).

Answer:

\(40\)