The area of a square is equal to the area of a rectangle. The ratio of the length and the width of the rectangle is 4: 1. If each edge of the square is 8 cm, what is the perimeter of the rectangle?

Correct option is B

Given:
Side of the square = 8 cm
Ratio of length to width of the rectangle = 4:1
Formula Used:
Area of square = $$s^2$$​​
Area of rectangle = Length × Width
Perimeter of rectangle = 2(Length + Width)
Solution:
Area of square = $$8^2 = 64 cm^2$$​​
Let the length of the rectangle be 4x and the width be x. The area of the rectangle is:
Area of rectangle = 4x × x =$$4x^2$$​​
Equating the area of the square and the area of the rectangle, we get:
64 = $$4x^2$$​​
​$$x^2 = 16$$​​

so x = 4 cm
Thus, the length of the rectangle = 4x = 4(4) = 16 cm and the width of the rectangle = 4 cm
Perimeter = 2(Length + Width) = 2(16 + 4) = 2(20) = 40 cm
Thus, the perimeter of the rectangle is 40 cm.