The bisector of the parallelogram ABCD meets the side BC at point K. Find the perimeter of the parallelogram
| February 9, 2021 | education
The bisector of the parallelogram ABCD meets the side BC at point K. Find the perimeter of the parallelogram if BK = 7, CK = 8.
The angle ВКА and KAD, since they are cross-lying angles at two parallel straight lines. Accordingly, we conclude that the ABC triangle is isosceles.
Further, by the definition of the bisector, we obtain that the angles KAD and BKA are equal. Consequently, the triangle AВK is also isosceles. Hence we find that the sides AB and BK are equal.
AB = BK = 7 cm.
Now let’s find the perimeter of the parallelogram:
2 * AB + 2 * BC = 2 * 7 + 2 * (BK + KС) = 14 + 2 * (7 + 8) = 14 + 2 * 15 = 14 + 30 = 44 cm.
Answer: 44 cm.
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