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.
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