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

Given the equation \( w(2w + 2)=40 \), expand the left - hand side:
\( 2w^{2}+2w = 40 \)
Divide the entire equation by 2 to simplify:
\( w^{2}+w=20 \)
Rearrange it to the standard quadratic form \( ax^{2}+bx + c = 0 \):
\( w^{2}+w - 20=0 \)

Step2: Factor the quadratic equation

We need to find two numbers that multiply to - 20 and add up to 1. The numbers are 5 and - 4.
So, \( w^{2}+w - 20=(w + 5)(w - 4)=0 \)

Step3: Solve for w

Set each factor equal to zero:
\( w+5 = 0\) or \( w - 4=0 \)
For \( w + 5=0 \), we get \( w=-5 \). But the width of a rectangle cannot be negative.
For \( w - 4=0 \), we get \( w = 4 \)

Answer:

4 units