Question

A rectangle's width is 5 feet less than its length. Write a quadratic function that expresses the rectangle's area in terms of its length.

A. A(l) = l(l)
B. (4(1) = w(w+5))
C. (A(1) = 12 - 5l)
D. (4(1) = 12 + 5l)

Answer 1

The correct quadratic function expressing the rectangle's area in terms of its length is, given by A(l) = w(w + 5). Thus the correct option is B.

Step-by-step explanation:

In the provided options, we need to identify the quadratic function that represents the area of the rectangle in terms of its length. Let's analyze option B: A(l) = w(w + 5).

In this quadratic function, w represents the width and l represents the length of the rectangle. The problem statement states that the width is 5 feet less than the length. Therefore, we can express the width as l - 5 . Substituting this into the quadratic function, we get A(l) = (l - 5)(l - 5 + 5) = (l - 5)(l), which simplifies to A(l) = l(l - 5). This quadratic expression correctly represents the area of the rectangle in terms of its length.

Now, let's consider why the other options are incorrect:

- Option A ( A(l) = l(l) is a simple linear expression and does not account for the given condition that the width is 5 feet less than the length.

- Options C and D are incorrect because they involve unrelated constants (12) and do not correctly represent the relationship between the length and width.

In conclusion, option B (A(l) = w(w + 5)) is the accurate quadratic function that expresses the rectangle's area in terms of its length, considering the given information about the relationship between the length and width of the rectangle.