One side of the rectangle was increased by 12 cm and received a square from this, the perimeter of the figure

One side of the rectangle was increased by 12 cm and received a square from this, the perimeter of the figure increased by 1.5 times. What is the side of the resulting square.

In such problems, it is convenient to use the method of introducing an unknown and solving an equation with this unknown.

Let the side of the square be a cm.Then the perimeter of the square is (4 * a) cm.Consequently, the perimeter of the rectangle will be (a + a + a – 12 + a – 12 = 4 * a – 24) cm. Based on the data obtained, compose and solve the equation:

4 * a = (4 * a – 24) * 1.5;
4 * a = 6 * a – 36;
6 * a – 4 * a = 36;
(6 – 4) * a = 36;
2 * a = 36;
a = 36: 2 = 18 (cm).

Answer: the side of the resulting square is 18 cm.