# 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.

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