A rectangle has an area of 120cm^2 and a perimeter of 52cm. What are its dimensions?

Length =

Width=

The dimensions of the rectangle are 20 cm of length and 6 cm of width or vice versa, the result will be the same.

Step-by-step explanation:

1. Let's check the information given in the question:

Area of the rectangle = 120 cm²

Perimeter = 52 cm

2. Let's use the area formula to calculate the length and width;

Length = x

Width = y

Area = x * y

120 = x * y

x = 120/y

3. Let's use the perimeter formula calculate the length and width

Perimeter = 2 * Length + 2 * Width

52 = 2 * (120/y) + 2y (Replacing Length by 120/y)

52 = 240/y + 2y

52 - 2y = 240/y

52y - 2y² = 240

52 y - 2y² - 240 = 0

26y - y² - 120 = 0

y² - 26y + 120 = 0 (multiplying by - 1 at both sides of the equation and now this is a quadratic equation)

(y - 20) * (y - 6) = 0 (factoring the quadratic equation)

y1 = 20

y2 = 6

The equation is asking me to find two whole numbers that added are 26 and multiplied are 120. Those numbers are 20 and 6, that are the length and the width of the rectangle.