The bisector of angle A of the parallelogram ABCD divides the side of CD in a ratio of 1: 3 counting

The bisector of angle A of the parallelogram ABCD divides the side of CD in a ratio of 1: 3 counting from the top of angle C. Find the sides if the perimeter is 84 centimeters.

Let us construct the bisector AM of angle A. Then cut 1 will be equal to cut 2.
AM secant with parallel ВС and АD, cut 2 and cut 3 crosswise, respectively, are equal. Hence it follows that kut 1 is equal to kut 3.
Consider the triangle ABM, it is isosceles and therefore AB is equal to BM.
BM: MS = 1: 3, let VM = x, then MS = 3x.
BC = BM + MC;
BC = x + 3x;
BC = 4x.
Since ABCD is a parallelogram, AB = CD, BC = AD.
P = AB + CD + BC + AD.
P = x + x + 4x + 4x;
10x = 84;
X = 8.4;
4x = 8.4 * 4 = 33.6.
AB = CD = 8.4cm, BC = AD = 33.6cm.