Answer:
[tex]x^2-4x+3[/tex]
[tex]63\ \text{sq. units}[/tex]
Step-by-step explanation:
l = Length = [tex]\dfrac{x^2-x-6}{x-5}[/tex]
w = Width = [tex]\dfrac{x^2-6x+5}{x+2}[/tex]
Area is given by
[tex]A=lw\\\Rightarrow A=\dfrac{x^2-x-6}{x-5}\times\dfrac{x^2-6x+5}{x+2}\\\Rightarrow A=\dfrac{x^2-3x+2x-6}{x-5}\times\dfrac{x^2-5x-1x+5}{x+2}\\\Rightarrow A=\dfrac{(x-3)(x+2)}{x-5}\times\dfrac{(x-5)(x-1)}{x+2}\\\Rightarrow A=(x-3)(x-1)\\\Rightarrow A=x^2-4x+3[/tex]
Area of the room is [tex]x^2-4x+3[/tex].
If [tex]x=10[/tex]
Area of the room
[tex]A=x^2-4x+3=10^2-4\times 10+3\\\Rightarrow A=63\ \text{sq. units}[/tex]
So, the amount of carpet needed would be [tex]63\ \text{sq. units}[/tex].
