Question

what is the value of r?
what is the length of segment ef?
units

Explanation:

Step1: Set up the equation

Since \(CF = DE\) (opposite sides of a parallelogram are equal), we have \(9r - 6=8r + 3\).

Step2: Solve for \(r\)

Subtract \(8r\) from both sides: \(9r-8r - 6=8r - 8r+ 3\), so \(r-6 = 3\).
Add \(6\) to both sides: \(r-6 + 6=3 + 6\), so \(r = 9\).

Step3: Find the length of \(EF\)

Since \(EF = CD\) (opposite sides of a parallelogram are equal), substitute \(r = 9\) into \(4r + 19\).
\(EF=4\times9+19=36 + 19=55\).

Answer:

The value of \(r\) is \(9\). The length of segment \(EF\) is \(55\) units.