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