Question

select the correct answer from each drop - down menu. the area of a rectangle is 91 square inches. if the length of the rectangle is 1 less than twice its width, write an equation that could be used to find the width, w, of the rectangle. \\(w^{2}+\square w +\square=0\\)

Explanation:

Step1: Set up area equation

The area of a rectangle is $\text{length} \times \text{width}$. Given length $=2w-1$, width $=w$, area $=91$.
$$w(2w - 1) = 91$$

Step2: Expand and rearrange to standard form

Expand the left side and subtract 91 from both sides to set the equation to 0.
$$2w^2 - w - 91 = 0$$

Answer:

The filled equation is $\boldsymbol{2w^2 + (-1)w + (-91) = 0}$ (or formatted as $\boldsymbol{2w^2 - w - 91 = 0}$)