The bisector of an acute angle of a parallelogram divides its side in a ratio of 2: 3, counting from the apex

The bisector of an acute angle of a parallelogram divides its side in a ratio of 2: 3, counting from the apex of its angle. The perimeter of the parallelogram is 42cm. Find his side.

1) Let in ABCD the side AB = a, the bisector AC1 of the angle <BAD divides the side BC, as 2: 3.

2) Triangle AC1D1 is isosceles, since angles <BAC1 = <C1AD <AC1D1 (straight line C1D1 is parallel to CD).

3) The AC side is divided into parts 2: 3; AB = C1D1 = a = 2 parts. C1C = 3 parts. Then the whole side BC = BC1 + C1C = 2 hours + 3 hours = 5 hours; side AB = BC1 = 2 h.

4) Perimeter ABCD = 2 h + 5 h + 2 h + 5 h = 14 h = 432 cm, whence 1 h = 42 cm: 14 = 3 cm.

5) Sides ABCD: AB = CD = 2 * 3 cm = 6 cm;

BC = AD = 5 * 3 cm = 15 cm.