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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