# The area of the rectangle is 108 cm2. Its length is 12 cm greater than the width.

**The area of the rectangle is 108 cm2. Its length is 12 cm greater than the width. Find the width of the rectangle. Find its length.**

Let x be the width of the rectangle. Since the length of the rectangle is twelve centimeters longer than the width, then the length of the rectangle is: x + 12 cm. The area of the rectangle is equal to the product of length and width: S = a * b. substituting our values, we get the equation: x (x + 12) = 108, x ^ 2 + 12x – 108 = 0. Find the discriminant of the quadratic equation:

D ^ 2 = b ^ 2 – 4ac = 122 – 4 1 (-108) = 144 + 432 = 576

Since the discriminant is greater than zero, the quadratic equation has two real roots:

x1 = -12 – √576 / 2 1 = (-12 – 24) / 2 = -36 / 2 = -18

x2 = -12 + √576 2 1 = (-12 + 24) / 2 = 12/2 = 6.

The width of the rectangle is 6 cm and the length is 6 + 12 = 18 cm.