Question

geometry with data analysis ic qtr b young continuous learning center - credit bearing (tutor) isosceles triangles identifying a leg length what is the length of \\( \overline { p r } \\)? units

Explanation:

Step1: Use the property of isosceles triangle

In an isosceles triangle \( \triangle PQR\) with \( \angle P=\angle Q\), the sides opposite to equal angles are equal. So \( PR = QR\).
Given \( PR = 5n\) and \( QR=32 + n\). Then \( 5n=32 + n\).

Step2: Solve the equation for \( n\)

Subtract \( n\) from both sides of the equation \( 5n=32 + n\).
\( 5n−n=32 + n−n\)
\( 4n=32\)
Divide both sides by \( 4\): \( n=\frac{32}{4}=8\).

Step3: Find the length of \( PR\)

Since \( PR = 5n\) and \( n = 8\), then \( PR=5\times8 = 40\).

Answer:

\( 40\)