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 the square if the area of the rectangle is 54 m2.

Let’s say one side of the rectangle is xm.

It is known that the area of a rectangle is 54 m². Since the area of a rectangle is equal to the product of its sides, the second side of this rectangle is 54 / x m.

If the first side is enlarged 3 times. then it became equal to 3 * x m, and the second was reduced by 2 times and it became equal to 54/2 * x m.

At the same time, it turned out to be a square, that is, the sides became equal:

3 * x = 54/2 * x,

3 * x = 27 / x,

3 * х² = 27,

x² = 9,

x = 3 (m) – one side of the rectangle.

3 * 3 = 9 (m) – side of the square.