One side of the rectangle is 4 cm longer than the other. If the smaller side of the rectangle is increased by 25%

One side of the rectangle is 4 cm longer than the other. If the smaller side of the rectangle is increased by 25%, and the larger side is reduced by 25%, then its area will decrease by 2cm². find the sides of this rectangle.

Let’s say that the length of one side of the rectangle is x cm, and the other is x + 4 cm.

If the smaller side is increased by 25%, then it becomes equal to:

x * (100 + 25) / 100 = 5 * x / 4 cm.

If the second side is reduced by 25%, then it becomes equal to:

(x + 4) * (100 – 25) / 100 = 3 * (x + 4) / 4.

Initially, the area of ​​the rectangle was:

x * (x + 4) = x² + 4 * x (cm²).

Then the area of ​​the rectangle was:

5 * x / 4 * 3 * (x + 4) / 4 = (15 * x² + 60 * x) / 16 (cm²).

We get the equation:

x² + 4 * x – (15 * x² + 60 * x) / 16 = 2,

16 * x² + 64 * x – 15 * x² – 60 * x = 32,

x² + 4 * x – 32 = 0.

The discriminant of this equation is:

4² – 4 * 1 * (-32) = 144.

Since x can only be a positive number, the problem has a unique solution:

x = (-4 + 12) / 2 = 4 (cm) – the smaller side of the rectangle.

4 + 4 = 8 (cm) – large side of the rectangle.