In the parallelogram MNPQ, the bisector MB divides the side NP in a ratio of 1: 5.

In the parallelogram MNPQ, the bisector MB divides the side NP in a ratio of 1: 5. Find the perimeter of the parallelogram if MQ = 16.8 cm.

Let the length of the segment BP be equal to X cm, then, by condition, the length of the segment NB = 5 * X cm.

Since in a parallelogram the opposite sides are equal, then NP = MQ = 16.8 cm, then X + 5 * X = 16.8.

6 * X = 16.8.

X = 16.8 / 6 = 2.8 cm.

Then NB = 5 * 2.8 = 14 cm.

Since, by condition, MB is the bisector of the angle, then the triangle MNB is isosceles, MN = NB = 14 cm.

Determine the perimeter of the parallelogram, P = 2 * (MN + MQ) = 2 * (14 + 16.8) = 61.6 cm.

Answer: The perimeter of the parallelogram is 61.6 cm.