In the rectangle CKMN, the bisector of angle C is drawn, which intersects the CM at point E

univerkov | April 3, 2021 | education

In the rectangle CKMN, the bisector of angle C is drawn, which intersects the CM at point E, and the length of the KE is 3 cm less than the length of ME. Find MN if the perimeter is CKMN = 51 cm.

1. The bisector CE of rectangle CKMН cuts off the isosceles triangle СEK from it (according to the properties of the rectangle). Therefore, KE = CK.

2. KM = СK + СK + 3 cm = 2СK + 3 cm, since KE is less than ME by 3 cm.

3. Opposite sides of the rectangle are equal (according to the properties of the rectangle).

СK = MN. KM = CН.

4. The perimeter of the rectangle is calculated by the formula:

2СK + 2KM = 51 cm.

СK + KM = 25.5 cm.

5.СK + 2СK + 3 = 25.5 cm.

СK = 7.5 cm.

MН = СK = 7.5 cm.

Answer: MН = 7.5 cm.

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