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.