Question

The length of a rectangle is 2 inches less than 3 times the width. Which equation describes the relationship between w, the width of the rectangle in inches, and A, the area in square inches?(1 point)
Responses

A=3w2−2w
cap A is equal to 3 w squared minus 2 w

A=2w2−3w
cap A is equal to 2 w squared minus 3 w

A=2w2−3
cap A is equal to 2 w squared minus 3

A=3w2−2

Answer 1

To find the equation that describes the relationship between \( w \) (the width) and \( A \) (the area) of the rectangle, we first need to establish the dimensions of the rectangle based on the given information.

1. The length \( l \) of the rectangle is given as:
\[
l = 3w - 2
\]
(since the length is 2 inches less than 3 times the width).

2. The area \( A \) of a rectangle is calculated using the formula:
\[
A = l \times w
\]

3. Now substituting the expression for the length into the area formula:
\[
A = (3w - 2) \times w
\]

4. Distributing \( w \):
\[
A = 3w^2 - 2w
\]

Thus, the equation that describes the relationship between the width \( w \) and the area \( A \) is:
\[
A = 3w^2 - 2w
\]

So the correct response is:
**A = 3w² − 2w.**