Question

identifying a side length
what is the value of ( r )?
what is the length of segment ( ef )?
feedback
opposite sides of a parallelogram are congruent. start
by solving for ( r ) by setting the expressions on opposite
sides equal to each other.

Explanation:

Step1: Use the property of parallelogram

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

Step2: Solve the equation for \(r\)

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

Step3: Find the length of segment \(EF\)

Substitute \(r = 9\) into the expression for \(EF\) (which is \(9r-6\)).
\(EF=9\times9 - 6\).
First, calculate \(9\times9=81\).
Then, \(81-6 = 75\).

Answer:

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