In parallelogram ABCD, bisectors AK and DM of angles A and D are drawn.

In parallelogram ABCD, bisectors AK and DM of angles A and D are drawn. If the perimeter of the parallelogram is 58 cm. KC = 5 cm, then the distance between points K and M is

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

Then, AB + BC = Ravsd / 2 = 58/2 = 29 cm.

Since AK is the bisector of the angle BAD, it cuts off the isosceles triangle ABK, AB = BK, from the parallelogram. Similarly, triangle DCM is isosceles, CD = CM.

Let AB = BK = CD = CM = X cm, then AB + BK + KС = 2 * X + 5 = 29 cm.

2 * X = 24 cm.

X = CD = CM = 12 cm.

Then MK = CM – KС = 12 – 5 = 7 cm.

Answer: Between points K and M 7 cm.