The bisector of angle A of parallelogram ABCD intersects side BC at point K.

The bisector of angle A of parallelogram ABCD intersects side BC at point K. Find the perimeter of the parallelogram if BK = 3, CK = 12.

From the properties of a parallelogram, we know that its opposite angles and sides are equal. Hence BC = AD;
BC = BK + CK;
BC = 3 + 12 = 15;
<BAK = <KAD (AK is the bisector and divides <DAB in half);
<DAK = <BKA (since they lie crosswise with parallel lines BC and AD and secant AK);
hence <BKA = <KAB, hence the triangle ABK is isosceles;
AB = BK = 3;
Perimeter ABCD = AB + BC + CD + DA = 3 +15 + 3 + 15 = 36;
Answer: 36;