In rectangle ABCD, the bisector of angle C divides side AD in a ratio of 2: 5. Find the ratio of the lengths of the sides

Let the bisector of angle C divides the side AD at point K.
AK / KD = 2/5
Angle СKD = КСВ (internal crosswise). Angle КСВ = KСD (СK – bisector by condition). We get that the angle КСD = angle СKD.
Consider triangle CDK, it is isosceles (angles at the base are equal).
KD = CD = AB = 5 pieces.
BC = AD = AK + KD = 2 + 5 = 7 parts.
We can write down the ratio of the lengths of the sides of the rectangle.
AB / DC = 5/7
Answer: The ratio of the lengths of the sides of the rectangle is 5/7.