The area of a rectangle whose width is 3 less than half its length can be found by the polynomial A(l)=12l2−3l

Question

. Which of the following are the two related quantities represented by this polynomial? Enter the number of the correct quantity.

Quantity #1: length of the rectangle and width of the rectangle

Quantity #2: width of the rectangle and perimeter of the rectangle

Quantity #3: perimeter of the rectangle and area of the rectangle

Quantity #4: area of the rectangle and length of the rectangle

(1 point)

Answer 1

To analyze the polynomial \( A(l) = 12l^2 - 3l \), we note that it represents the area of a rectangle, where \( l \) is the length of the rectangle. According to the problem statement, the width \( w \) of the rectangle is described as "3 less than half its length," which can be expressed as:

\[ w = \frac{1}{2}l - 3 \]

The area \( A \) of a rectangle is given by:

\[ A = \text{length} \times \text{width} = l \times w \]

Substituting the expression for \( w \):

\[ A = l \left( \frac{1}{2}l - 3 \right) = \frac{1}{2}l^2 - 3l \]

It seems there might have been a discrepancy in the polynomial provided, as multiplying out the widths results in a different coefficient compared to the given polynomial \( A(l) = 12l^2 - 3l \). Let's assume \( A(l) \) is supposed to represent a direct relationship with respect to \( l \) regardless of the constant.

The quantity that directly corresponds to \( A(l) \) when evaluated concerning length and width is:

• Quantity #1: length of the rectangle and width of the rectangle.

Thus, the most appropriate choice from the perspectives described is Quantity #1.