The sides of a square all have a side length of y. Write a simplified area function in terms of y for a rectangle whose length is twice the side length of the square and whose width is 2 units longer than the side length of the square.
Part A: Express both the length and the width of the rectangle as a function of a side of the square.
(1 point)
Let y be the side length of the square.
Length of the rectangle = 2y
Width of the rectangle = y + 2
Therefore, the length and width of the rectangle as a function of y are:
Length = 2y
Width = y + 2
Part B: Write a function to represent the area of the rectangle in terms of the sides of the square. (1 point)
The area of a rectangle is given by the formula:
Area = Length x Width
Substitute the values of length and width in terms of y:
Area = (2y) x (y + 2)
Area = 2y^2 + 4y
Therefore, the function to represent the area of the rectangle in terms of the sides of the square is:
Area = 2y^2 + 4y