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 :)
