# One side of the rectangle is 9cm larger, the other. Find the sides of a rectangle if its area is 112cm².

To solve this problem, we need to write an equation. Let’s recall the formula for the area of a rectangle. The area of the rectangle is equal to the product of the length and the width. S = a * b, where a is the length and b is the width. Let the width of the rectangle be x cm, then its length is (x + 9) cm. Knowing that the area is 112 cm ^ 2, we compose the equation.

x (x + 9) = 112;

x ^ 2 + 9x-112 = 0;

We got a quadratic equation, we calculate the discriminant.

a = 1; b = 9; c = -112.

D = b ^ 2-4ac = 81 + 4 * 112 = 81 + 448 = 529;

x = -b + √D / 2a = -9 + 23/2 = 7;

x = -b-√D / 2a = -9-23 / 2 = -32 / 2 = -16.

We got two answers -16 and 7, since the side of the rectangle cannot be negative, then the width is 7 cm, and the length is 7 + 9 = 16 cm.

Let’s check.

S = 7 * 16 = 112 cm ^ 2.

Answer: 7 cm, 16 cm.