Question

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!

Answer 1

Explanation:

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

(2w - 7) inches

The formula for determining the area of a rectangle is expressed as

Area = length × width

Therefore, the function, A(w) that gives the area as a function of the width us

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 = 0

2w² + 8w - 15w - 60 = 0

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

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

w = - 4 or w = 15/2

Since the width cannot be negative, then

Width = 15/2 = 7.5 inches