How to change the area of a rectangle if one side is reduced by three times, and the other is increased by 3 times?

Let the sides of this rectangle be a and b. Then its area is equal to:

S = a * b.

Let a1 be the side of the new rectangle, enlarged three times, then a1 = a * 3, b1 – the side of the new rectangle, reduced three times: b1 = b / 3.

The area of the resulting rectangle is:

S1 = a1 * b1 = (a * 3) * (b / 3) = a * b = S.

Therefore, if one of the sides of the rectangle is enlarged three times, and the other is reduced three times, the area of the rectangle will not change.