The area of a rectangle can be found by using this formula: Area = Length • Width
The question gives us the area and the width, so all we need to look for is the length. To do this, we manipulate the formula so we are solving for length, like so: Length = Area / Width
Area = x^2 -9
Width = x-3
Length = unknown
Now, we plug in what we know (Area and Width) into the formula for Length:
Length = (x^2 - 9) / (x - 3)
x^2 - 9 simplifies to (x - 3)(x+3) so we are left with: Length = (x - 3)(x + 3) / (x - 3) and we see that (x - 3) cancels out
The final answer is that *Length = x + 3*
To check your work, you can plug in each part into the formula for area and see if the answers match
