If the length of the rectangle is increased by 2 dm, and the width is reduced by 5 dm

If the length of the rectangle is increased by 2 dm, and the width is reduced by 5 dm, then you will get a square, the area of which will be less than the area of the rectangle by 50 dm2. Determine the area of the square.

Let us denote by the variable x the length of the side of the square.

Therefore, we can express the length of the rectangle in terms of (x – 2), and we can express the width of the rectangle in terms of (x + 5).

Knowing by the condition of the problem that the area of the square is less than the area of the rectangle by 50 dm2, we draw up an equation and determine the side of the square:

(x – 2) (x – 5) – x ^ 2 = 50;

x ^ 2 – 2x + 5x -10 – x ^ 2 = 50;

3x = 60;

x = 20.

Let’s define the area of a square with a side of 20 decimeters:

20 * 20 = 400.

Answer: The area of the square is 400 dm2.