# ABCD-parallelogram; BE-bisector of angle ABC; perimeter ABCD-48 cm; AB is 3 cm larger

September 12, 2021 | education

| **ABCD-parallelogram; BE-bisector of angle ABC; perimeter ABCD-48 cm; AB is 3 cm larger than AD. Find the sides of the parallelogram.**

Since BE is the bisector of angle ABC, the angle ABE = CBE.

A parallelogram has opposite sides equal and parallel.

Then the angle CBE = AEB as criss-crossing angles at the intersection of parallel straight lines BC and AD secant BE. Then the angle ABE = AEB, and the triangle ABE is isosceles, AE = AB.

Let the length of the segment AE = X cm, then AD = (X – 3) cm.

AB = AE = SD = X cm, BC = AD = (X – 3) cm.

Ravsd = 2 * (AB + BC) = 2 * (X – 3 + X) = 48 cm.

4 * X = 48 + 6 = 54.

X = AB = CD = 54/4 = 13.5 cm.

AD = BC = 13.5 – 3 = 10.5 cm.

Answer: The lengths of the sides of the parallelogram are 10.5 cm and 13.5 cm.

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