In parallelogram ABCD, the bisector AE divides side BC into segments Be and EC. Moreover, BE: EC = 3: 1.

| January 15, 2021 | education

In parallelogram ABCD, the bisector AE divides side BC into segments Be and EC. Moreover, BE: EC = 3: 1. The perimeter of the parallelogram is 56cm. Find the sides of the parallelogram.

Since AE is the bisector of the angle, the angle BAE = DAE. The angle BEA = DAE as the cross-lying angles at the intersection of parallel lines AD and BC secant AE, therefore, triangle ABE is isosceles, AB = BE.
Let the length of the segment EC = X cm, then, by condition, the length of the segment BE = 3 * X cm.
AB = BE = 3 * X cm. The length of the segment BC = BE + EC = 3 * X + X = 4 + X cm.
Then the perimeter of the parallelogram will be: Rvasd = 2 * (AB + BC) = 2 * (3 * X + 4 * X) = 14 * X.
14 * X = 56.
X = 56/14 = 4 cm.
AB = CD = 3 * 4 = 12 cm.
BC = AD = 4 * 4 = 16 cm.
Answer: The sides of the parallelogram are 12 cm and 16 cm.



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