In parallelogram ABCD, the bisector of angle A intersects side BC at point N. Find the perimeter

In parallelogram ABCD, the bisector of angle A intersects side BC at point N. Find the perimeter of the parallelogram if BN = 13cm, NC = 5cm.

Since ABCD is a parallelogram, its opposite sides are equal and parallel.

Then the angle АНВ = DАН as criss-crossing angles at the intersection of parallel lines АD and ВС secant АН.

Then in the triangle ABН the angle ВAН = ВНA, which means that the triangle ABН is isosceles, AB = ВН = 13 cm.

Side length ВС = ВН + СН = 13 + 5 = 18 cm.

Since the opposite sides of a parallelogram are equal, its perimeter is:

Ravsd = 2 * (AB + BC) = 2 * (13 + 18) = 62 cm.

Answer: The perimeter of the parallelogram is 62 cm.