One side of the rectangle is 9 cm larger than the other. find the sides of the rectangle if its area is 112cm2.

To find the lengths of the sides of a rectangle, compose and solve the equation.

Denote by variable x – the length of one of the sides of the rectangle, then the length of the second side can be written as (x + 9) cm.

The area of a rectangle is equal to the product of the lengths of the sides of the rectangle.

S = a * b;

x (x + 9) = 112;

x ^ 2 + 9x – 112 = 0;

D = b ^ 2 – 4ac = 92 – 4 * 1 * (-112) = 81 + 448 = 529;

We are looking for the roots of the equation:

x1 = (-b + √D) / 2a = (-9 + 23) / 2 = 14/2 = 7;

x2 = (-b – √D) / 2a = (-9 – 23) / 2 = -32/2 = -16. – the root is not suitable.

The length of one of the sides is 7 cm, 7 + 9 = 16 cm.