Chapter 4 - Section 4.1 - Properties of a Parallelogram - Exercises - Page 188: 7

$QR = 11$ $RN = 11$ $QN = 22$

The diagonals of a parallelogram bisect each other. Therefore the point R is the midpoint of $\overline{QN}$ We can find the value of $x$: $QR = RN$ $2x+3 = x+7$ $x = 4$ We can find $QR$: $QR = 2x+3 = (2)(4)+3 = 11$ We can find $RN$: $RN = x+7 = 4+7 = 11$ We can find $QN$: $QN = QR + RN = 11 + 11 = 22$