Question

identifying a leg length
what is the length of (overline{pr})?
units

Explanation:

Step1: Recognize the triangle type

The triangle \( \triangle PQR \) has two equal angles at \( P \) and \( Q \), so it is an isosceles triangle with \( PR = QR \).

Step2: Set up the equation

Since \( PR = 5n \) and \( QR = 32 + n \), we set \( 5n = 32 + n \).

Step3: Solve for \( n \)

Subtract \( n \) from both sides: \( 5n - n = 32 + n - n \), which simplifies to \( 4n = 32 \). Then 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