Answer:
[tex]AD=31\ units[/tex]
Step-by-step explanation:
we know that
In a Parallelogram opposite sides are equal in length and opposite angles are equal in measure
so
in this problem
To be a parallelogram
[tex]AD=BC[/tex]
[tex]AB=DC[/tex]
we have
[tex]AD=3x+7[/tex] -----> equation A
[tex]BC=5x-9[/tex] ------> equation B
equate equation A and equation B
[tex]3x+7=5x-9[/tex]
solve for x
[tex]5x-3x=7+9[/tex]
[tex]2x=16[/tex]
[tex]x=8\ units[/tex]
Find the length of segment AD
[tex]AD=3x+7[/tex]
[tex]AD=3(8)+7=31\ units[/tex]
