QN = 28
Solution:
Given MNPQ is a parallelogram.
QT = 4x + 6 and TN = 5x + 4
To find the length of QN:
Let us solve it using the property of parallelogram.
Property of Parallelogram:
Diagonals of the parallelogram bisect each other.
Therefore, QT = TN
⇒ 4x + 6 = 5x + 4
Arrange like terms together.
⇒ 6 – 4 = 5x – 4x
⇒ 2 = x
⇒ x = 2
Substitute x = 2 in QT and TN
QT = 4(2) + 6 = 14
TN = 5(2) + 4 = 14
QN = QT + TN
= 14 + 14
QN = 28
The length of QN is 28.