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

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

Step2: Factor the quadratic equation

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

Step3: Solve for \(w\)

Set each factor equal to zero:
\(w+5 = 0\Rightarrow w=-5\) (rejected since width cannot be negative)
\(w - 4=0\Rightarrow w = 4\)

Answer:

4 units