Question

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

Explanation:

1. First, assume the figure is a parallelogram (since there are equal - side - length markings which are common in parallelograms). In a parallelogram, opposite sides are equal.

• Let's assume that \(9r - 6=4r + 19\) (assuming these are opposite - side lengths).
• Solve the equation \(9r-4r=19 + 6\).
• Combine like terms: \(5r=25\).
• Divide both sides by 5: \(r = 5\).

1. Now, if we assume \(EF = 8r+3\) (from the figure).

• Substitute \(r = 5\) into the expression for \(EF\).
• \(EF=8\times5+3=40 + 3=43\).

Answer:

What is the value of \(r\)? \(5\)
What is the length of segment \(EF\)? \(43\) units