In rectangle ABCD, the bisector of angle A intersects side BC into segments BK = 6 cm and KC = 3 cm.

In rectangle ABCD, the bisector of angle A intersects side BC into segments BK = 6 cm and KC = 3 cm. Find the perimeter of the rectangle.

1. The bisector AK divides a rectangle into two geometric shapes – a quadrangle

AKCD and triangle ABK.

According to the properties of the rectangle, this triangle is isosceles.

Therefore, BK = AB = 6 centimeters.

2. BC = BK + CK = 6 + 3 = 9 centimeters.

3. In a rectangle, according to its properties, the sides are opposite each other

are equal. Therefore, AB = CD = 6 centimeters, BC = AD = 9 centimeters.

4. Calculate the perimeter (P) of a given rectangle:

P = 2 (6 + 9) = 30 centimeters.

Answer: The perimeter of the given rectangle is 30 centimeters.