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

July 24, 2021 | education

| **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.**

We draw up an equation in which we write the width of the rectangle as x cm.

Since its length is 12 cm longer, it will be equal to: x + 12 cm.

Since the area of a rectangle is the product of its sides, we get the following expression:

x * (x + 12) = 108.

x ^ 2 + 12 * x = 108.

We get a quadratic equation:

x ^ 2 + 12 * x – 108 = 0.

D ^ 2 = (12) ^ 2 – 4 * 1 * (-108) = 144 + 432 = 576.

D = √576 = 24.

x = (-12 + 24) / 2 = 12/2 = 6 cm (rectangle width).

x + 12 = 6 + 12 = 18 cm (length).

Answer: 6 and 18 cm.