In the rectangle ABCD, segment CK is the bisector of angle C. Calculate the perimeter of the rectangle.

In the rectangle ABCD, segment CK is the bisector of angle C. Calculate the perimeter of the rectangle. If AK is 4 cm, KD is 6 cm.

1. Calculate the length of the side AD of the rectangle:

AD = AK + DK = 4 + 6 = 10 cm.

2. The bisector drawn from the vertex C divides the angle ВСD in half. Therefore, the angle

DCК = 90 °: 2 = 45 °.

3. The angle at the vertex K of the right-angled triangle CKD is equal to:

180 ° – 90 ° – 45 ° = 45 °.

The angles at the base of the SC are equal. Therefore, triangle CKD is isosceles. Means,

КD = СD = 6 cm.

4. The perimeter of the rectangle ABCD is 2AD + 2CD = 2 x 10 + 2 x 6 = 20 + 12 = 32 cm.

Answer: the perimeter of the rectangle ABCD is 32 cm.