Question

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

Explanation:

Step1: Set up the equation

In a parallelogram, opposite sides are equal. So, \(9r - 6=8r + 3\).

Step2: Solve for \(r\)

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

Step3: Find the length of \(EF\)

Since \(EF=9r - 6\) (or \(EF = 8r+3\), we use \(r = 9\)).
Substitute \(r = 9\) into \(9r - 6\): \(9\times9-6=81 - 6=75\).

Answer:

The value of \(r\) is \(9\).
The length of segment \(EF\) is \(75\) units.