The perimeter of the rectangle is 60 cm. If one side of it is reduced by 5

The perimeter of the rectangle is 60 cm. If one side of it is reduced by 5 cm and the other is increased by 3 cm, then its area will decrease by 21 square cm. Find the sides of the rectangle.

Let us denote the lengths of the sides of this rectangle through x and y.

Then the area of ​​this rectangle will be x * y.

If one side of this rectangle is reduced by 5 cm, and the other is increased by 3 cm, then the area of ​​the resulting rectangle will be (x – 5) * (y + 3).

According to the condition of the problem, as a result of this, the area of ​​the rectangle will decrease by 21 square meters. see, therefore, we can write the following relation:

(x – 5) * (y + 3) = x * y – 21.

Simplifying this ratio, we get:

x * y + 3x – 5y – 15 = x * y – 21;

3x – 5y = 15 – 21;

3x – 5y = -6;

3x = 5y – 6;

x = (5/3) y – 2.

According to the condition of the problem, the perimeter of the rectangle is 60 cm.

Therefore, the sum of the lengths of the sides of this rectangle is 60/2 = 30 cm and we can draw up the following equation:

(5/3) y – 2 + y = 30.

We solve the resulting equation:

(5/3) y + y = 30 + 2;

(8/3) y = 32;

y = 32 / (8/3);

y = 3 * 32/8;

y = 3 * 4;

y = 12 cm.

Knowing y, we find x;

x = (5/3) y – 2 = (5/3) * 12 – 2 = 5 * 4 – 2 = 20 – 2 = 18 cm.

Answer: the sides of the rectangle are 18 cm and 12 cm.