In a rectangle, one side is 4 cm larger than the other, the area is 45 cm ^ 2 find the sides of the rectangle.

Let the width of the rectangle be x cm, then the length of the rectangle is (x + 4) cm (if the length is 4 cm more than the width, then add 4 cm to the width). By the condition of the problem, it is known that the area of a rectangle (the area of a rectangle is equal to the product of its length and width; S = ab) is equal to x (x + 4) cm ^ 2 or 45 cm ^ 2. Let’s make an equation and solve it.

x (x + 4) = 45;

x ^ 2 + 4x = 45;

x ^ 2 + 4x – 45 = 0;

D = b ^ 2 – 4ac;

D = 4 ^ 2 – 4 * 1 * (-45) = 16 + 180 = 196; √D = 14;

x = (-b ± √D) / (2a);

x1 = (-4 + 14) / 2 = 10/2 = 5 (cm) – width;

x2 = (-4 – 14) / 2 = -18/2 = -9 – length may not be negative;

x + 4 = 5 + 4 = 9 (cm) – length.

Answer. 5 cm, 4 cm.