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

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

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

A=2w2−3w

1 answer

To find the equation that describes the relationship between the width \( w \) of the rectangle and the area \( A \), we start by expressing the length in terms of the width.

Given that the length \( l \) is 2 inches less than 3 times the width \( w \), we can write the equation for length as:

\[ l = 3w - 2 \]

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

\[ A = l \times w \]

Substituting the expression for length into the area formula, we get:

\[ A = (3w - 2) \times w \]

This simplifies to:

\[ A = 3w^2 - 2w \]

Therefore, the equation that describes the relationship between \( w \) and \( A \) is:

\[ \boxed{A = 3w^2 - 2w} \]

This corresponds to the option:

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