The length of the rectangle is 13 cm longer than its width. The area of the rectangle is 140 cm 2.

The length of the rectangle is 13 cm longer than its width. The area of the rectangle is 140 cm 2. Find the perimeter of the rectangle.

Let the width of the rectangle be x cm, then its length is x + 13 cm, and the area of the rectangle is 140 cm ^ 2. Since the area of a rectangle can be calculated as the product of length and width, then

x * (x + 13) = 140.

Equation x ^ 2 + 13x – 140 = 0

by Vieta’s theorem, the roots are equal

x (1) = -20 – does not make sense,

x (2) = 7 (cm) – the width of the rectangle.

Its length is 7 + 13 = 20 (cm).

The perimeter of a rectangle is calculated as twice the sum of the length and width:

2 * (7 + 20) = 54 (cm).