Answer:
Width of the rectangle is (x-5)
Step-by-step explanation:
We know that, the product of length and width gives the area of the rectangle.
The area of a rectangle is given as,
[tex]\Rightarrow \text{Area of rectangle}=\text{Length}\times \text{Width}[/tex]
[tex]\Rightarrow \text{Width}=\dfrac{\text{Area of rectangle}}{\text{Length}}[/tex]
Factoring the area,
[tex]=x^2-2x-15[/tex]
[tex]=x^2-5x+3x-15[/tex]
[tex]=x(x-5)+3(x-5)[/tex]
[tex]=(x+3)(x-5)[/tex]
Putting it in the equation,
[tex]\Rightarrow \text{Width}=\dfrac{(x+3)(x-5)}{(x+3)}=(x-5)[/tex]
