One side of the rectangle is 2 cm larger than the other. Find the sides if the area is 120 cm².

Let the length of one side of the rectangle be x centimeters, then the length of its second side is (x + 2) centimeters. We know that the area is 120 cm ^ 2. Let’s make the equation:

x * (x + 2) = 120;

x ^ 2 + 2x – 120 = 0;

a = 1, b = 2, c = -120;

D = b ^ 2 – 4 * a * c = 4 – 4 * 1 * (-120) = 4 + 480 = 484 (the discriminant is greater than zero, then this quadratic equation has two roots);

x = (-b + √ D) / 2 * a = (2 + √484) / 2 * 1 = (2 + 22) / 2 * 1 = 24/2 = 12;

x = (-b – √ D) / 2 * a = (2 – √484) / 2 * 1 = -20/2 = -10 does not satisfy the condition of the problem;

12 + 2 = 14 centimeters – the length of the other side.

Answer: 12 centimeters; 14 centimeters.