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
Part B: Write a function to represent the area of the rectangle in terms of the sides of the square.
Part A:
Since the length of the rectangle is twice the side length of the square, we can express it as 2y.
Since the width of the rectangle is 2 units longer than the side length of the square, we can express it as y + 2.
Part B:
The area of a rectangle is given by the formula A = length * width.
Substituting the expressions for the length and width from Part A, we have:
A = (2y) * (y + 2)
Simplifying, we can distribute and then combine like terms:
A = 2y^2 + 4y