ABCD is a parallelogram. AO is the bisector of angle A, divides side BC into segments equal to 12

ABCD is a parallelogram. AO is the bisector of angle A, divides side BC into segments equal to 12 cm and 2 cm. Find the perimeter of ABCD.

The solution of the problem:

1) The perimeter of the parallelogram is:

P = 2 (a + b).

2) The bisector of the angle of the parallelogram cuts off the isosceles triangle from it.

3) Therefore, BO = BA = 12 cm, by the property of the bisector of the parallelogram angle.

4) Calculate BC.

12 + 2 = 14 cm.

5) Now let’s define the perimeter of ABCD.

2 (12 + 14) = 2 * 26 = 52 cm

Answer: The perimeter of parallelogram ABCD is 52 cm.