The bisectors of angles A and D of parallelogram ABCD meet at point M, which lies on side BC

The bisectors of angles A and D of parallelogram ABCD meet at point M, which lies on side BC. Find the sides of the parallelogram if its perimeter is 36cm.

ABCD – aralelogram,
AM – the first bisector of the bisector
DM – second bisector
angle MAD = angle AMB since they are internal versatile angles = angle BAM,
triangle ABM is isosceles,
AB = BM = CD = x,
angle ADM = angle DMС as internal versatile = angle MDC, triangle MDC isosceles, CD = MC = x
BC = BM + MC = x + x = 2 x = AD
perimeter = x + 2x + x + 2x, 36 = 6x, x = 6 = AB = CD, ADВС = 2 * 6 = 12