If one side of the square is reduced by 2 cm and the other by 4 cm, then its area will decrease by 7 cm. Find the side of the square.

Suppose we have a square with a side whose length is x cm.

Then the area of ​​this square is x ^ 2 cm2.

If one side of this square is reduced by 2 cm, and the other side is reduced by 4 cm, then you get a rectangle with sides (x – 2) cm and (x – 4) cm.

The area of ​​this rectangle will be equal to (x – 2) (x – 4) cm2.

If we compare the areas of this square and the resulting rectangle, then the area of ​​the rectangle will be 7 cm2 less than the area of ​​the square.

(x – 2) (x – 4) = x ^ 2 – 7.

x ^ 2 – 4x – 2x + 8 = x ^ 2 – 7.

x ^ 2 – x ^ 2 – 4x – 2x = -7 – 8.

-6x = -15.

x = (-15): (-6).

x = 2.5 (cm).

Answer: the length of the side of the square is 2.5 cm.