In parallelogram ABCD, the bisector of an acute angle C intersects side AD and point M

In parallelogram ABCD, the bisector of an acute angle C intersects side AD and point M, AM = 2cm MD = 8, find the perimeter of parallelogram ABCD.

Angle BCM = MCD, since CM is the bisector of angle C.

Angle CMD = BCM, since the angles are crossing, at the intersection of line CM parallel lines BC and AD.

Since the angles MCD and CMD are equal, the triangle CDM is isosceles and the length of CD is equal to MD.

The sides of the parallelogram are equal: AD = 2 + 8 = 10 cm, CD = 8 cm.

Find the perimeter of the parallelogram:

P = 2 * (AD + CD) = 2 * (10 + 8) = 2 * 18 = 36 cm.

Answer: 36 cm.