One side of the rectangle is 3 cm larger and the other 2 cm smaller than the side of the square.

One side of the rectangle is 3 cm larger and the other 2 cm smaller than the side of the square. Find the side of the square if its area is 1 cm² larger than the area of the rectangle

Let’s say that the side of the square is x cm.

Then, according to the condition of the problem, one of the sides of the rectangle will be equal to x + 3 cm, and the second, respectively, x – 2 cm.

The area of such a rectangle will be equal to:

(x + 3) * (x – 2) = x² – 2 * x + 3 * x – 6 = x² + x – 6 (sq. cm).

As you know, the area of a square with side x is equal to x², which means that, according to the condition of the problem, the following equation can be drawn up:

x² + x – 6 = x² – 1,

x = 6 – 1,

x = 5 (cm).

Answer: 5 cm.