One side of the rectangle was enlarged 3 times and the other was reduced 2 times and got a square.

One side of the rectangle was enlarged 3 times and the other was reduced 2 times and got a square. What is the side of a square if the area of a rectangle is 54 m2?

Let’s denote the first side of this rectangle by x, and the second side by y.

According to the condition of the problem, the first side of this rectangle was enlarged 3 times, and the second was reduced 2 times and got a square.

Since the lengths of the sides of the square are equal, we can write the following ratio:

3x = y / 2,

from which we obtain y = 6x.

By the condition of the problem, the area of ​​the rectangle is 54 m ^ 2, therefore, we can write the following ratio:

x * y = 54.

Substituting the value y = 6x into this ratio, we get the equation:

x * 6x = 54.

We solve the resulting equation:

6x ^ 2 = 54;

x ^ 2 = 54/6;

x ^ 2 = 9;

x ^ 2 = 3 ^ 2;

x = 3 m.

Knowing the first side of the rectangle, we find the side of the square:

3x = 3 * 3 = 9 m.

Answer: the side of the square is 9 m.