The length of a rectangle is 7 inches less than twice the width, w, of the rectangle.

Part A:
The quadratic function A(w) represents the area, A, in square inches, of the rectangle for a given value of w. What function gives the area as a function of the width?

Part B:
If the area of the rectangle is 60 square inches, what is the width of the rectangle?

Please explain and say why your answer is reasonable! 30 points.

Step-by-step explanation:

Let w represent the width of the rectangle.

The length of a rectangle is 7 inches less than twice the width, w, of the rectangle. It means that the length is (2w - 7) inches

Part A

The function that gives the area as a function of the width is

A(w) = w(2w - 7)

Part B:

If the area of the rectangle is 60 square inches, it means that

w(2w - 7) = 60

2w² - 7w = 60

2w² - 7w - 60 = 0

2w² + 8w - 15w - 60 = 0

2w(w + 4) - 15(w + 4) = 0

2w - 15 = 0 or w + 4 = 0

w = 15/2 or w = - 4

Since w cannot be negative, then

w = 15/2 = 7.5 inches