In the rectangle SKMN, the bisector of the angle C is drawn, which intersects the side KM at point E

In the rectangle SKMN, the bisector of the angle C is drawn, which intersects the side KM at point E, and the length of the segment KE is 3 cm less than the length ME. find МN if the perimeter of CKMN is 51 cm.

1. ME = KE + 3 cm.

2. The bisector CE divides the rectangle into two geometric shapes. One of them is isosceles ΔSKE. Its two sides SK and KE are equal.

3. CK = MN.

4. KM = KE + ME. We substitute here (KE + 3) instead of ME:

KM = KE + KE + 3 = 2KE + 3. KE is replaced by MN:

KM = 2MN +3.

5. We calculate the length of the side MN using the formula for calculating the perimeter (P) of a rectangle:

P = 2SK + 2KM = 51 cm.

6. We replace in this expression CK by MN and KM by 2MN +3:

2МN + 4МN + 6 = 51 cm.

6МN = 45 cm.

MN = 7.5 cm.