In parallelogram mnpq, side mn is seven inches longer than twice the length of side np if the perimeter of mnpq is 68 inches then determine the length of np

Opposite sides of a parallelogram are the same length. Let the length of side np = x inches. Side qm is then also x inches. The problem gives the length of side mn in terms of side np as (2*x) + 7 inches. Side pq is then also (2*x) + 7 inches. The perimeter is the sum of all four sides. x + x + [ (2*x) + 7] + [ (2*x) + 7], or 6x + 14 inches. We are given the perimeter measure, so 6x + 14 = 68. Subtract 14 from both sides: 6x = 54. Divide both sides by 6: x = 9 inches. Thus the length of side np is 9 inches.

Perimeter of a parallelogram = 2 (a+b)

Perimeter of parallelogram mnpq = 68 inches

mn is seven inches longer than twice the length of side np

let the length of np = x

length of mn = 2x + 7

Now,

p = 2 (2x+7+x)

68 = 4x + 14 + 2x

68 = 6x + 14

6x = 68 - 14

6x = 54

x = 9

Thus, the length of np is 9 inches.