The area of a rectangle that is 5cm longer than its width is 126cm square. Find the sides of the rectangle.

From the condition, we know the area of the rectangle, it is equal to 126 cm ^ 2. We know that the length is 5 cm longer than the width.

Let us denote by the variable x cm – the width of the rectangle, then the length is (x + 5) cm.

The formula for finding a rectangle looks like this S = a * b;

x (x + 5) = 126;

x ^ 2 + 5x – 126 = 0;

D = b ^ 2 – 4ac = 5 ^ 2 – 4 * 1 * (-126) = 25 + 504 = 529.

We look for the roots of the equation by the formulas:

x1 = (-b + √D) / 2a = (-5 + 23) / 2 = 18/2 = 9;

x2 = (-b – √D) / 2a = (-5 – 23) / 2 = -28/2 = -14.

Width cannot be negative.

Width is 9 cm, length (9 + 5) = 14 cm.