Final answer:
The width of the rectangle is found by dividing the given area expression by the length expression, which results in the width being x+1.
Step-by-step explanation:
If the area of the rectangle is represented by the equation x²-4x-5, and the length of the rectangle is x-5, we can find the width of the rectangle in terms of x by using the formula for the area of a rectangle, which is Area = Length × Width. In this case, the equation for the area given is equivalent to the product of the length and the width of the rectangle. Hence, we can express the width as Width = Area ÷ Length. When we substitute the given values, we have:
Width = (x²-4x-5) ÷ (x-5)
To find the width, we will need to divide the quadratic equation by x-5. We can factor the quadratic equation to get:
x²-4x-5 = (x-5)(x+1)
Now we divide by x-5:
Width = ((x-5)(x+1)) ÷ (x-5) = x+1
Therefore, the width of the rectangle in terms of x is x+1.