Answer:
19 units.
Step-by-step explanation:
Consider the below figure attached with this question.
From the below figure it is given that MN=PQ.
It is given that MP = 6x – 5, QR = 3x + 1, and RN = 6.
Since non parallel sides are equal, therefore it is an isosceles trapezoid.
The diagonals of an isosceles trapezoid are equal.
[tex]MP=QN[/tex]
[tex]MP=QR+RN[/tex]
Substitute the given values.
[tex]6x-5=3x+1+6[/tex]
[tex]6x-5=3x+7[/tex]
[tex]6x-3x=5+7[/tex]
[tex]3x=12[/tex]
[tex]x=4[/tex]
The value of x is 4.
[tex]QN=MP=6x-5=6(4)-5=24-5=19[/tex]
Hence, the measure of QN is 19 units.
