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

January 13, 2021 | education

| **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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