Answer:
length = x+6
width = x-6
Step-by-step explanation:
The area of rectangle is:
[tex] \displaystyle \large{ A= l \times w}[/tex]
where A is area, l is length and w is width.
We know the area of this rectangle or table since we are given A = x^2-36.
First, substitute A = x^2-36 in.
[tex] \displaystyle \large{ {x}^{2} - 36 = lw}[/tex]
Then we factor x^2-36, use the difference of two squares:
[tex] \displaystyle \large{ (x + 6)(x - 6) = lw}[/tex]
Compare the terms.
First, we have to understand that length is always longer or greater or have more values than width.
Hence length cannot be x-6 and width cannot be x+6 either.
Thus:
[tex] \displaystyle \large{length = x + 6} \\ \displaystyle \large{width = x - 6}[/tex]
