Increase one side of the rectangle by 3 times, and reduce the other by 2 times and get a square.

Increase one side of the rectangle by 3 times, and reduce the other by 2 times and get a square. What is the side of the square if the area of the rectangle is 54m

1. Take the side of the square for x. Then the length of the rectangle is:
x * 2 = 2x (cm);
2. Width of the rectangle:
x / 3 (cm);
3. Knowing that the area of the rectangle is equal to the product of the length and width, we compose the equation:
2x * (x / 3) = 54;
2x ^ 2/3 = 81;
x ^ 2 = 81;
x = 9;
The length of the square is 9 centimeters;
Answer: 9 cm.