Question

1. find the length of pr, if \\( \triangle pqr \\) is isosceles with \\( pq\cong rq \\).

Explanation:

Step1: Set up the equation for the equal sides

Since \(PQ\cong RQ\), we have \(7x - 13=5x + 11\).

Step2: Solve the equation for \(x\)

Subtract \(5x\) from both sides: \(7x-5x - 13=5x-5x + 11\), which simplifies to \(2x-13 = 11\).
Add \(13\) to both sides: \(2x-13 + 13=11 + 13\), so \(2x=24\).
Divide both sides by \(2\): \(x = 12\).

Step3: Find the length of \(PR\)

Substitute \(x = 12\) into the expression for \(PR\) (\(PR=2x - 2\)).
\(PR=2\times12-2\).
First, calculate \(2\times12 = 24\), then \(24-2=22\).

Answer:

\(22\)