Question

The length of a rectangle is four meters less than twice it's width. If the area of the rectangle is 96 square meters what is the width?

Answer 1

Answer: (I'm sorry if this is not the right answer)

The width = 8 meters

Step-by-step explanation:

The length: a (m)

The width: b (m)

We cannot have a negative length and a negative width: a>b>0

Eq. I: a=2b-4

Eq. II: ab=96

Substitute the value of a from Eq. I into Eq. II: (2b-4).b=96

Solve for b:

(2b-4).b=96

2$b^{2}$-4b-96=0

$b^{2}$-2b-48=0

$b^{2}$+6b-8b-48=0

b.(b+6)-8.(b+6)=0

(b+6).(b-8)=0

b=8; b=-6

As mentioned above, b>0. Therefore, b=8

Conclusion: if the area of the rectangle is 96 square meters then its width is 8 meters.