Question

What must the length of segment AD be for the quadrilateral to be a parallelogram?

Answer 1

The answer is 31 units

Answer 2

`AD=31\ units`

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

`AD=BC`

`AB=DC`

we have

`AD=3x+7` -----> equation A

`BC=5x-9` ------> equation B

equate equation A and equation B

`3x+7=5x-9`

solve for x

`5x-3x=7+9`

`2x=16`

`x=8\ units`

Find the length of segment AD

`AD=3x+7`

`AD=3(8)+7=31\ units`