Answer: NP = 9 inches
Explanation:
In a parallelogram, the opposite sides are equal.
If the length of the longer side is MN, it means that the length of the two opposite longer sides is 2MN.
If the length of the shorter side is NP, it means that the length of the two opposite shorter sides is 2NP.
The perimeter is 2MN + 2NP
If the perimeter of MNPQ is 68 inches, it means that
2MN + 2NP = 68- - - - - - - - - - - -1
In parallelogram MNPQ, side MN is seven inches longer than twice the length of side NP. It means that
MN = 2NP + 7- - - - - - - - - - -2
Substituting equation 2 into equation 1, it becomes
2(2NP + 7) + 2NP = 68
4NP + 14 + 2NP = 68
4NP + 2NP = 68 - 14
6NP = 54
NP = 54/6
NP = 9 inches