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,
\(\Rightarrow \text{Area of rectangle}=\text{Length}\times \text{Width}\)
\(\Rightarrow \text{Width}=\dfrac{\text{Area of rectangle}}{\text{Length}}\)
Factoring the area,
\(=x^2-2x-15\)
\(=x^2-5x+3x-15\)
\(=x(x-5)+3(x-5)\)
\(=(x+3)(x-5)\)
Putting it in the equation,
\(\Rightarrow \text{Width}=\dfrac{(x+3)(x-5)}{(x+3)}=(x-5)\)
