One side of the rectangle is 5 m larger than the other and its area is 126 m2. find the sides of the rectangle.

1. Let one side of the rectangle be x, then the second side is x + 5;
2. The area of a rectangle is calculated by multiplying its two adjacent sides. Let’s make the equation:
x * (x + 5) = 126;
x ^ 2 + 5x – 126 = 0;
3. We are looking for the discriminant:
D = 5 ^ 2 – 4 · 1 · (-126) = 25 + 504 = 529;
4. The discriminant is greater than 0, which means that the quadratic equation has two roots:
x1 = (-5 – √529) / 2 * 1 = (-5 – 23) / 2 = -14;
x2 = (-5 + √ 529) / 2 * 1 = (-5 + 23) / 2 = 9;
5. Since the side cannot be negative, then x1 is meaningless. Therefore, one side is 9 m, and the second is 9 + 5 = 14;
6. Answer: 9 meters and 14 meters.