The perimeter of a rectangle is 60 cm. If one side of it is reduced by 5 cm and the other is increased by 3 cm

The perimeter of a 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 cm squared. Find the sides of the rectangle.

To solve the problem, you can draw up a system of equations, since the perimeter of the rectangle is 60 cm, and also that if you reduce one side of it by 5 cm and increase the other by 3 cm, then its area will decrease by 21 cm².
Let’s denote by x and y the sides of the rectangle:
2 * (x + y) = 60
x * y – 21 = (x – 5) (y + 3);
x + y = 30
xy – 21 = xy + 3x – 5y – 15;
x = 30 – y
-7 = 3 * (30 – y) – 5y;
-7 = 90 – 3y – 5y;
8y = 97;
y = 12.125;
x = 30 – 12.125 = 17.875.
Answer: 17.875 cm is the length of the rectangle, 12.125 cm is its width.