One side of the rectangle is 5 m larger than the other, and its area is 84m2. Find the sides of the rectangle.

Let one side of the rectangle be x meters, then the second side of the rectangle is (x + 5) meters. By the condition of the problem, it is known that the area of a rectangle is x (x + 5) m ^ 2 (the area of a rectangle is equal to the product of its sides) or 84 m ^ 2. Let’s make an equation and solve it

x (x + 5) = 84;

x ^ 2 + 5x = 84;

x ^ 2 + 5x – 84 = 0;

D = b ^ 2 – 4ac;

D = 5 ^ 2 – 4 * 1 * (-84) = 25 + 336 = 361; √D = 19;

x = (-b ± √D) / (2a);

x1 = (-5 + 19) / (2 * 1) = 14/2 = 7 (m) – one side of the rectangle;

x2 = (-5 – 19) / 2 = -12 – side length cannot be negative;

x + 5 = 7 + 5 = 12 (m) – the second side of the rectangle.

Answer. 7 m; 12 m.