One side of the rectangle is 9 cm larger than the other. Find the sides of a rectangle if its area is 112 cm ^ 2

Let x be one side of the rectangle, then x + 9 is the other side of the rectangle.

Formula for the area of a rectangle:

S = a * b, where S is the area of the rectangle, a is the length of the rectangle, b is the width of the rectangle.

112 = x * (x + 9) = x² + 9 * x;

x² + 9 * x = 112;

x² + 9 * x – 112 = 0; a = 1, b = 9, c = -112;

D = b² – 4 * a * c = 81 + 448 = 529 = 23²;

x1 = (-b – √D) / 2 * a = (-9 – 23) / 2 = -16 – does not match the condition.

x2 = (-b + √D) / 2 * a = (- 9 + 23) / 2 = 7 cm – one side of the rectangle.

7 + 9 = 16 cm – the other side.

Answer: 7 and 16 cm