Question

Find QN. Please show all the work on how you got your answer

Answer 1

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.