A rectangle's length is 4 more than its width. If the area is 96, what is the width?

Let the width be $w$, so the length is $w+4$. The area is $w(w+4)=96$, so $w^2+4w-96=0$, which factors as $(w+12)(w-8)=0$. A width cannot be negative, so $w=8$, choice D. Check: the length is $12$ and $8\cdot12=96$. Choice B ($12$) is the length, not the width. Choice A ($6$) gives a length of $10$ and an area of $60$. Choice C ($10$) gives a length of $14$ and an area of $140$. Reject the negative root $-12$ because a dimension must be positive.