In the parallelogram ABCD, the bisector of angle D intersects the side AB at point P.

In the parallelogram ABCD, the bisector of angle D intersects the side AB at point P. The segment AP is 6 times less than BP. Find the perimeter of the parallelogram if AB = 14cm.

1. The bisector DP of the parallelogram ABCD cuts off the triangle ADP from it, which is isosceles (according to the properties of the parallelogram). Therefore, AP = AD.

2. AR + BP = AB = 14 cm.

AR is 6 times less than BP according to the condition of the problem. That is, BP = 6AP.

AR + 6AP = 14 cm.

7AP = 14 cm.

AP = 2 cm.

AD = 2 cm.

3. Considering that the opposite sides of the parallelogram ABCD are equal, its perimeter is calculated by the formula:

2AB + 2AD = 2 x 14 + 2 x 2 = 32 cm.

Answer: the perimeter of the parallelogram ABCDD = 32 cm.