Question

the length of a rectangle is 1 less than twice the width.
the area of the rectangle is 28 square feet.
which equation represents the situation?
2w² - w + 28 = 0
2w² - w - 28 = 0
2w² + w - 28 = 0
2w² + w + 28 = 0
what is the length of the rectangle?
done

Explanation:

Step1: Define Variables

Let \( w \) be the width of the rectangle. The length \( l \) is 1 less than twice the width, so \( l = 2w - 1 \).

Step2: Use Area Formula

The area of a rectangle is \( A = l \times w \). We know \( A = 28 \), so substitute \( l = 2w - 1 \) into the area formula:
\( 28 = (2w - 1) \times w \)

Step3: Expand and Rearrange

Expand the right - hand side: \( 28 = 2w^{2}-w \)
Subtract 28 from both sides to set the equation to zero: \( 2w^{2}-w - 28 = 0 \)

Answer:

\( 2w^{2}-w - 28 = 0 \) (the second option in the dropdown menu)