Question

a rectangles length is 2 units more than twice its width. its area is 40 square units. the equation w(2w + 2)=40 can be used to find w, the width of the rectangle. what is the width of the rectangle? 4 units 5 units 10 units 12 units

Explanation:

Step1: Expand the equation

\[

$$\begin{align*} w(2w + 2)&=40\\ 2w^{2}+2w&=40 \end{align*}$$

\]

Step2: Rearrange to standard quadratic - form

\[2w^{2}+2w - 40=0\]
Divide through by 2: \(w^{2}+w - 20 = 0\)

Step3: Factor the quadratic equation

We need two numbers that multiply to - 20 and add up to 1. The numbers are 5 and - 4.
So, \((w + 5)(w - 4)=0\)

Step4: Solve for w

Setting each factor equal to zero gives:
\(w+5 = 0\) or \(w - 4=0\)
\(w=-5\) or \(w = 4\)
Since width cannot be negative, we discard \(w=-5\)

Answer:

4 units