In parallelogram ABCD, the bisector of angle C intersects side AD at point N, AN = 6, ND = 10. Find the perimeter of the parallelogram.
1. The bisector CN of the parallelogram ABCD cuts off the isosceles triangle CND from it. Therefore, ND = CD = 10 centimeters.
2. AD = AN + DN = 6 + 10 = 16 centimeters.
3. Opposite sides of a parallelogram are equal. Therefore, AB = CD = 10 centimeters. BC = AD = 16 centimeters.
4. The total length of all sides of the parallelogram (perimeter) = AB + CD + BC + AD = 10 + 10 + 16 + 16 = 52 centimeters.
Answer: the total length of all sides of the parallelogram (perimeter) is 52 centimeters.
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