# In the rectangle KMNP, the bisector of the angle MKP is drawn, which intersects the side MN at point E

In the rectangle KMNP, the bisector of the angle MKP is drawn, which intersects the side MN at point E. Find the side KP if ME = 11 cm, and the perimeter of the rectangle KMNP is 62 cm.

1. We calculate the value of the angle ЕКР, taking into account that the bisector divides the angle К of the rectangle into two equal parts:

90 °: 2 = 45 °.

2. We calculate the value of the MEK angle:

180 ° – 90 ° – 45 ° = 45 °

3. Triangle AOB is isosceles, since the angles MEK and EKP at the base of the CM are equal.

Therefore, ME = KM = 11 cm.

4. Considering that in the rectangle the sides opposite to each other are equal, we calculate the length of the side КР:

62 = 2ME + 2KP;

KР = (62 – 2 x 11) / 2 = 40/2 = 20 cm.

Answer: the length of the side of the KR rectangle is 20 cm.

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