# In rectangle ABCD, the bisector of angle A divides the side BC into segments BK = 7cm and KC= 9cm.

In rectangle ABCD, the bisector of angle A divides the side BC into segments BK = 7cm and KC = 9cm. Find the perimeter of the rectangle.

1. The bisector AK divides the angle at the vertex A in half:
angle ВAK = 90 °: 2 = 45 °.
2. Angle AKВ = 180 ° – 90 ° – 45 ° = 45 °. The angles at the base of AB are equal. Therefore the triangle
AVK is isosceles. Therefore, AB = ВK = 7 centimeters.
3. Calculate the length of the BC side of the rectangle:
BC = ВK + КС = 7 + 9 = 16 centimeters.
4. Given that the sides of the rectangle opposite each other are equal, we calculate its perimeter:
2BC + 2 AB = 16 + 7 = 23 centimeters.
Answer: The perimeter of the rectangle is 23 centimeters.

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