Given that quadrilateral pqrs is a parallelogram, find the value of qs.

The shape is a parallelogram, so we know that the diagonals of the parallelogram bisect each other.

So QS is bisected by PR.

That means,

3x - 7 = 6x - 31

Now solve for x.

3x - 7 = 6x - 31
-7 = 3x - 31
24 = 3x
8 = x

Now use 8 for x and find the measures of the equal sides of the diagonal QS.

3x - 7 
3(8) - 7
17

6x - 31
6(8) - 31
17

Now we will add both 17's and find the length of QS.

QS = 17 + 17 = 34

SO the length of diagonal QS is 34

Hope this helps :)