The area of the rectangle is 12 m². What are the sides of a rectangle if one of them is 4 m larger than the other?

Width – x. Length – x + 4. The area is 12 cm2 and is calculated by the formula: S = a * b, where a – length, b – width.

Let’s make the equation:

12 = x * (x + 4).

12 = x2 + 4x.

x2 + 4x – 12 = 0.

According to Vieta’s theorem:

x1 + x2 = -p, where p = -4.

x1 * x2 = q, where q = -12.

The roots of the equation are equal: x1 = -6 (does not fit, the length cannot be negative), x2 = 2 (correct).

Width of the rectangle: x = 2 cm.

Rectangle length: x + 4 = 2 + 4 = 6 cm.

Answer: The length of the rectangle is 6 cm, the width is 2 cm.