The area of a rectangle is $x^2 + 4x – 12$. What is the length and width of the rectangle?
The solution says the main idea is to factor $x^2 + 4x -12$.
So, since $-12 = -2 \times 6$ and $-2 + 6 = 4$, it can be written as $x^2 + 4x – 12 = (x – 2)(x + 6)$
since the length is usually the longer value, the length is $6$ and the width is $-2$.
I don't understand the logic to this solution at all. I understand $\text{length} \times \text{width} = \text{area}$, but outside of this information I don't understand how they got to this solution from the given information in the problem.
Best Answer
That is incorrect. Many rectangles, with different lengths and widths, can have the same area. Example: $2\times3 = 1\times6 = \pi\times\frac6\pi$
Also, the area is a function of $x$; if $x$ is not given, then the area is not given!
And width can't be negative.
Where did you find this "solution"? It's very wrong.
EDIT1
Perhaps they just wanted you to factor the expression. Then the "answer" would have the length $(x+6)$ , and the width $(x-2)$ . But even this isn't unique; it could be $(2x+12)$ and $(\frac12 x-1)$ . Someone gave you a bad question.