In the BCDE parallelogram, the bisector of angle B intersects the side DE at point K, with DK

univerkov | September 11, 2021 | education

In the BCDE parallelogram, the bisector of angle B intersects the side DE at point K, with DK = 4, EK = 12. Find the perimeter of the parallelogram.

1. The bisector BK of the parallelogram ВСDE cuts off the triangle ВЕК from it, which is isosceles. Therefore, KE = BE = 12 centimeters.

2. DE = DK + EK = 4 + 12 = 16 centimeters.

3. Opposite sides of a parallelogram are equal. Therefore, CD = BE = 12 cm, BC = DE = 16 centimeters.

4. The total length of all sides of the parallelogram (perimeter) = СD + BE + BC + DE = 12 + 12 + 16 + 16 = 56 centimeters.

Answer: the total length of all sides of the parallelogram (perimeter) is 56 centimeters.

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