The bisectors of the angles of the parallelogram adjacent to one side divide the opposite side of the parallelogram
July 29, 2021 | education|
The bisectors of the angles of the parallelogram adjacent to one side divide the opposite side of the parallelogram into three equal segments. Find the adjacent sides of the parallelogram if its perimeter is 88cm and the bisectors do not intersect.
Since the bisectors AH and DK divide the BC side into three equal segments, we denote their length by X cm. BH = HK = CK = X cm, then BC = (BH + HK + CK) = 3 * X cm.
The bisectors AH and DK form isosceles triangles ABH and CDK, AB = BH = X cm, CD = CK = X cm.
The perimeter of the parallelogram is: Ravsd = 2 * (AB + BC) = 2 * (X + 3 * X) = 8 * X = 88 cm.
X = 88/8 = 11 cm.
AB = CD = 11 cm.
AD = BC = 3 * 11 = 33 cm.
Answer: The adjacent sides of the parallelogram are 11 cm and 33 cm.
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