The bisector of angle A of the parallelogram ABCD divides the side BC into segments BE

The bisector of angle A of the parallelogram ABCD divides the side BC into segments BE and EC so that BE: EC = 3: 1. Find the sides of the parallelogram if you know that. its perimeter is 42cm.

1) Consider a triangle ABE, in which the angles at the base of AE are equal (<BAE = <BEA), since <BAE = <EAD, since AE is the bisector of angle <BAD, but <EAD = <BEA, as angles for parallel aircraft and AD.

2) Hence, AB = BE, as sides in an isosceles triangle ABE.

3) Let us denote by the condition BE: EC = 3: 1, BE = 3 * x, EC = x, AB = BE = 3 * x.

4) Perimeter ABCD = AB + BC + CD + AD = 3 * x + 4 * x + 3 * x + 4 * x = 14 * x = 42 cm, whence x = 42 cm / 14 = 3 cm.

5) Sides ABCD: AB = CD = 3 * x = 3 * 3 cm = 9 cm; BC = AD = 4 * x = 4 * 3 cm = 12 cm.